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Full text of "International Meeting on Astrophysics & Elementary Particles common problems"

ISSN: 0391 - «04I 

ACCADEMIA NAZIONALE DEI LINCEI 

ANNO CCCLXXV11 - 1980 



CONTRIBUTI DEL 

CENTRO LINCEO INTERDISCIFUNAKE 

DI SCIENZE MATEMATICHE E LORO AFPLICAZIONI 

N. 53 



INTERNATIONAL MEETING ON 

ASTROPHYSICS 

AND ELEMENTARY PARTICLES, 

COMMON PROBLEMS 

(Rome, 21 st -23 fd February 1980) 




ROMA 

ACCADEMIA NAZIONALE DEI LINCEI 

1980 



ISSN: 03?1 - 8041 

ACCADEMIA NAZIONALE DEI LINCEI 

ANNO CCCLXXVII - 1980 



CONTRIBUTI DEL 

CENTRO LINCEO INTERDISCIPLINARE 

DI SCIENZE MATEMATICHE E LORO APPLICAZIONI 

N. 53 



INTERNATIONAL MEETING ON 

ASTROPHYSICS 

AND ELEMENTARY PARTICLES, 

COMMON PROBLEMS 

(Rome, 21 st -23 rd February 1980) 




ROMA 

ACCADEMIA NAZIONALE DEI LINCEI 

1980 




«MARVES» - Roma 



On February 21, 22 and 23, 1980 the International Congress 
"Astrophysics and Elementary Particles , Common Problems" was 
held in Rome at the Centro Linceo Interdi sciplinare. The fun- 
damental problems common to the two disciplines , Astrophysics 
and Physics , were dealt with. -This congress can be considered 
the concrete translation of the need for discuss ion between 
phys icists of the two branches , already expre ssed at congresses 
in Italy and abroad. In fact the recent advance s in Astrophys ics 
and Particle Physics have revived or rather inflamed the tra- 
ditional scientific exchange between the two branches , new 
fields of research having opened up in recent years causing 
as trophys icis t s to consult subnuclear phys icists and vice 
versa. 

In fact recent developments infield theories, the theories 
of Gauge in particular , point to the quest for a complete uni- 
fication of fundamental forces, but this re sear ch seems to in- 
exorably lead towards energy fields in the elementary inter- 
actions lying far beyond those which can be direct ly studied 
with the accelerators of this century. 

On the other hand, in accordance with the theory of the 
Big Bang, this very high energy per particle was a reality 
during the initial stage of expansion of the universe , so that 
still today it is possible to detect traces of this important 
initial phase - traces which cannot be deciphered without a 
knowledge of the most recent discover ie s of particle physics. 

The more specific reasons for this congress emerge from 
the reports presented. These are the direct test imony of an 
exciting meeting which participants hope to see repeated in the 
not too distant future. 

We are grateful to all those speakers who accepted the 
invitation to participate and appreciate the many reques ts to 
revise the text and, clarify the methods and terminology inorder 
to permit a more general understanding. 



We hope that this congre s s will permit scholars of the one 
branch to better understand the argument s of the other, thus 
leading to that reciprocal under standing so neces sary to sci- 
ence. If, then, such an occasion leads to new synthesis and 
stimulates new re sear ches , those who worked towards the success 
of this congre ss will be fully rewarded. 



NICOLA CABIBBO, University of Rome 
NICOLO' DALLAPORTA; University of Padua 
LIVIO GRATTON, University of Rome 
FRANCO PACINI, University of Florence 
GIORGIO SALVINI, University of Rome 



3 - 



Nei giorni 21, 22. e 23 di Febbraio 1980 si e" tenuto in 
Roma, nella sede del Centro Linceo Interdisciplinare , un Con- 
ve gno Internazionale dedicato alia Astrofisica ed alia Fisica 
delle particelle elementari . In esso si sono trattati , come chia- 
risce il titolo ufficiale: "Astrophysics and Elementary Parti- 
cles, Common Problems", i problemi aperti e fondamentali comu- 
ni alle due discipline. Questo incontro si puo' cons iderare la 
traduzione concreta di un desiderio sorto da discussioni tra i 
cultori delle due discipline , e reiterato in occas ione di mol- 
ti incontri in Italia e all ' estero . Infatti i recenti e note- 
volis s imi progre s si in As trof isica e nella Fisica delle parti- 
celle hanno riacceso o piuttosto' infiammato il tradizionale 
scambio scientifico tra le due comunita', alle quali si sono a- 
perti in questi anni nuovi campi di ricerca, ove gli astrofi- 
sici debbono r ivolgersi ai subnuc leari e viceversa. 

Infatti gli sv iluppi , coronat i da fondamentali succe s s i , 
delle teorie di campo, in particolare delle teorie di Gauge, 
puntano alia ricerca di una unificazione completa delle forze 
fondamentali ; ma questa ricerca sembra ine sorabilmente portare 
verso domini di energia nelle interazioni elementari che stan- 
no ben al di la'di quelli che si possono o potranno studiare 
dire ttamente con gli accelerator i di questo secolo. 

D'altra parte, in accordo con la teoria del Big Bang, que- 
ste altissime energie per particella furono re alt a' durante la 
fase iniziale di espansione dell 'Universo, sicche' puo' essere 
ancora oggi possibile trovare tracce di questa importante fase 
iniziale. Tracce che non si possono decifrare senza la cono- 
scenza dei piu recenti risultati della fisica delle particel- 
le. 

Le piu' precise ragioni di questo incontro emergono dalle 
relazioni. qui riportate. Possiamo permetterci di affermare che 
esse sono la tes t imonianza diretta di un incontro eccitante , 
che gli intervenuti si augurano possa ripetersi a non lunga 



s cadenza . 

Siamo grati a tutti gli oratori che hanno r ispos to all 'in- 
vito ed alia pesante richiesta di riordinare il testo e di ren- 
dere chiari all' altra parte i propri metodi ed il loro linguag- 
gio. Noi speriamo che questo Conve gno possa permettere ad ogni 
studioso di un campo di capire meglio il discorso dell'altro 
campo, per raggiungere una comprens ione reciproca de I la quale 
la Scienza ha grande bisogno. Se poi da confronti come questo 
verra' I'occasione di nuove sintesi e la spinta a nuove ricer- 
che sperimentali , questo sara' il massimo premio cui puo' aspi- 
rare chi ha lavorato alia riuscita del nostro incontro . 



NICOLA CABIBBO, Universita di Roma 
NICOLO' DALLAPORTA, Universita' di Padova 
LIVIO GRATTON, Universita' di Roma 
FRANCO PACINI, Universita di Firenze 
GIORGIO SALVINI, Universita di Roma 



PROGRAM 



FIRST SESSION 

Thursday, 21 8t February - 9,30 a.m. 

GIORGIO SALVINI: "Why this Meeting". 

SHELDON L.GLASHOW: "Astrophy si cs and Elementary Particles. 
Introductory Talk". 

JOHN N. BAHCALL: "Solar Neutrinos". 

MALVIN RUDERMAN: "Superdense Ma tter and Elementary Particle 
Physics". 

SECOND SESSION 

Thursday, 21 8t February - 3,30 p.m. 

GARY STEIGMAN: "As trophy si cal Constraints on Neutrino 
Physics" . 

ETTORE FIORINI: "Neutrino Experiments in the Laboratory. 
Open Problems". 

LUCIANO MAIANI: "Neutrino Oscillations". 



THIRD SESSION 

Friday, 22 nd February - 9,30 a.m. 

DENNIS W. SCIAMA: "The Anisot ropy of th e Cosmic Black Body 
Radiation and its Meaning". 

JOHN ELLIS: "Grand Unified Theories and the Very Early 

Uni verse" . 
GIUSEPPE COCCONI-. "Big. and smaller Bangs suggesting new 

Physics 1 ' 



- 6 



FOURTH SESSION 

Friday, 22 nd February - 3,30 p.m. 

BERNARD J. CARR : "The Origin of Entropy and Galaxy Forma- 
tion". 

CARLO RUBBIA: "Experiments with Elementary Particles re- 
lated to Cosmology: Neutrino Oscillations and Proton 
Li fetime" . 

RICCARDO GIACCONI: "X-ray Astronomy - Recent Results". 

MILLA BALDO-CEOLIN : : "Search for neutron antineutron oscil- 
lations" . 



FIFTH SESSION 

Saturday, 23 rd February - 9,30 a.m, 

REMO RUFFINI: "On the Magnetosphere of collapsed Stars". 

FRANCO PACINI: "The Activity of Galactic Nuclei". 

ALFONSO CAVALIERE: "Physics of the compact Sources: in 
active galactic Nuclei and Quasars". 

NICOLA CABIBBO: "Concluding Remarks". 



- 7 - 

FIRST SESSION 
21 st February 1980 - 9.30 a.m. 

Chairman: Luigi Radicati di Brozolo 



GIORGIO SALVINI 
WHY THIS MEETING 



The basis of this meeting is the consciousness that we, 
astrophysicists and elementary particle physicists, are study- 
ing the same world with the same aims and methods and mathema- 
tics, and with similar instruments 

Of course, the idea of a common discussion between stu- 
dents of nuclear and subnuclear physics and students of the 
Universe, is neither original nor unexpected: this has gone on 
for all this century , through extremely fruitful collaboration. 
Perhaps the beginning of this collaboration goes even further 
back in time: one could take as a significant date, to show the 
full maturity of astrophysics, the year 1868, when the astro- 
nomer J.N. Lockyer discovered a new element, Helium, in solar 
photosphere. As is known, he noticed a characteristic yellow 
line (D 3 ) close to lines Z)i and Z) 2 of sodium. The element Helium 
was discovered on the earth only 25 years later, by Sir William 
Ramsey. This in a way was a prelude to the anticipations of 
cosmic rays with respect to the accelerating machines in dis- 
covering new mesons and baryons. 

But now, in these last three or four years, we have at 
least a threefold coincidence of facts- which makes our meeting 
interes ting: 



8 



- Elementary particle physicists are approaching a general syn- 
thesis or unification: however in the process of this syn- 
thesis, the possible elementary particles have been growing 
in mass and have arrived at limits which shall never be reached 
in the laboratories on Earth. Even more, it seems difficult 
to establish how many particles there are, and how heavy. 
Astrophysicists try to help us with the Big Bang, and tell us 
that 10' seconds after the beginning (at 10 degrees) of 
the Universe all particles were there. We can therefore try 
to induce from Big Bang and its history the total elementary 
architecture of our world. 

- The second point is that the pro ton could have a limited life 

(still long, 10 -10 years, well beyond the life of the 
Universe). This is strongly suggested by the present unified 
theories, and the astrophysicists certainly do not dislike 
the idea. This instability of the proton comes in a sense to 
change our present understanding. In fact, we have believed 
until now in the stability of the proton as Linneo believed 
in the stability of the species in the 19th century. But the 
instability of the proton now seems to introduce evolution 
and history in the matter, as Lamarck started to do in the 
description of life on Earth in his Philosophie Zoologique. 
This new situation is destined perhaps to increase the links 
between elementary physicists and astrophysicists in the feel- 
ing of a common unrepeatable adventure. 

- Cosmic ray results are rather persistent in suggesting that 
there are new thresholds in hadronic behaviour, when we go 
to superhigh energies: something which tends to limit the 
certainty of the representation of the world of the elementary 
particles, as established with the discoveries of present day 
accelerating machines. 

The threefold coincidence I have quoted has an output to- 
ward thehighest theoretical s pecu lations , as we shall hear dur- 
ing these two days: perhaps, we have never been as successful 



and as uncertain as today, in all the history of fundamental 
physics. So, it is not strange that more than one person (I do 
not know who started this exactly) initiated the idea of a meet- 
ing like ours, and the Centro Linceo Interdisciplinare, for its 
interdisciplinary nature, was the natural place for it in Eu- 
rope. I must anyway point out that the agreement from elementary 
particle physicists to this meeting was rather enthusiastic, 
and not less from astrophysicists. But after enthusiasm, a com- 
mon thought came, which was underlined by many of us: just be- 
cause of the great appeal of these perspectives, we feel that 
our meeting should not be intended as the celebration of the 
interdisciplinary astrophysics - particle area, but rather as 
an occasion for a critical appraisal of the situation . Thi s will 
probably emerge from the discussions , to which we shall dedicate 
ample space. 

This meeting arose perhaps mostly as an invitation from 
particle physicists toward astrophysicists, and this for some 
good precise reasons. In fact, many of these subnuclear physi- 
cists, like me, have been invited in these last years to give 
opinions on what to do next. For instance: what could we expect 
from pp at the highest energies? What do we expect from LEP, 
the future electron positon colliding ring of at least two hun- 
dred GeV in the center of mass? How dangerous may it be to for- 
get hadron physics in Europe? What could' be the interest of a 
future 20 TeV colliding ring? 

So , - I was among these egotists, and I thought that to have 
a discussion on the common problems in h . e. particles and astro- 
physics was a broad and good way to have a perspective on these 
problems. 

Let me try to be more specific, by recalling some of them: 

— How many neutrinos are there in the Universe? At least those 
with a low mass? Well, this is interesting for the experiment 
we are doing at CERN, for instance, p+p—Z +.... In fact, 
if they are too many, then the rate of decays in e e and 



- 10 - 

fj. (J. will change and it could go dangerously down. I will 
therefore be very attentive in listening to this classical 
problem, to see how sound the conclusions are. 

- How many new masses, gluons, quarks, higss could we expect? 
Can we hope to create in future all possible existing parti- 
cles with machines, for instance 20 TeV colliding hadron ma- 
chines? (We could have been rather sure ten years ago). If 
not, and the spectroscopy of masses will extend well beyond 
these limits, then the Big Bang becomes, as it has been said, 
our future accelerator. But how much of rhetoric, how much of 
truth is contained in this statement? 

- Passing to experimental activities and techniques: how much 
do we have in common? Could it be profitable if high energy 
laboratories were less separated from space research labora- 
tories? This I will also try to understand in this meeting. 

Before closing, let me remind that we, the astrophysicists 
and the elementary particle physicists, have another thing in 
common: a kind of loneliness with respect to other sciences, 
which in one way or the other enter more directly in the prac- 
tical life of a modern society. Mutual discussion will help to 
reduce this feeling of ours, and it will also help the desire 
and curiosity for pure and disinterested knowl edge, which is the 
message that we must transmit to the present sometimes des- 
pairing human society. 



11 - 



SHELDON L. GLASHOW 



ASTROPHYSICS AND ELEMENTARY PARTICLES 
INTRODUCTORY TALK (,) 



We seem to have developed a theory which gives a correct 
and complete description of parti cle phenomena from zero energy 
to energies of order 100 GeV and beyond. In this "low-energy" 
domain, only a few well-characterized surprises may await dis- 
covery: the t quark, the nature of 6 -decay, the Higgs boson, 
etc. At higher energies, a desert is expected wherein no es- 
sentially new phenomena are expected up to the unifying energy 

14- 

U^IO GeV. This "prediction" of the theory will soon be put 
to the test as accelerators are designed and constructed to 
operate in the multi-TeV domain. Aside from the observation of 
W and Z and perhaps a new heavy quark, physi cs at Isabelle should 
be as monumentally dull as physics at 1SR. 

Of course, there is a wealth of new physical systems lying 
at or above the unification energy M. These particles are simply 
too heavy to be produced directly, and they are too unstable to 
be found lying about. They cannot be studied directly. Fortu- 
nately, there do exist a few narrow windows through which the 
new physics may be dimly glimpsed. The superheavy particles can 
produce small effects at ordinary energies: we shall discuss 
such phenomena as proton decay and neutrino osci llations. More- 
over, the superheavy particles were once of crucial importance 
in the early stages of the big bang: the ultimate accelerator. 
Here is the most direct confrontation of particle physics and 
astrophysics. 



(*) Research supported in part by the National Science Foundation under 
Grant No. PHY77-22864. 



12 



My talk.this con ference, and our two conjoined disciplines 
no longer consider merely the nature of matter in the micro- 
and macroworlds. We are as much concerned with the very history 
of matter: how it came into being and how it will ultimately 
decay. Within an infinity of logarithmic time, our fields are 

- 40 

centered on the tiny slice in which we live: 10 seconds to 

10 seconds. This is the Age of Baryons. 

Once upon a time, the great disco ve ries of particle physics 
could be accomplished in simple experiments which did not de- 
pend upon large particle accelerato rs . This is the way the elec- 
tron, the neutrino, the positron, the muon , and strange parti- 
cles were found. In the last three decades , things have changed. 
We could never have learned about quarks, QCD and the electro- 
weak theory by studying those particles that are "at hand". 
Rather, we go to great lengths to produce artificially the most 
bizarre and short lived forms of matter. Only thus have we 
learned about CP violation, the complex energy-level spectrum 
of nucleons, meson spectroscopy .heavy quarks, neutral currents, 
the tau lepton, and even atomic parity violation. 

The active (accelerator) field is very much alive, and we 
are not to predict its imminent demise. Hadron -hadron collisions 
are now studied at c.m. energies of 60 GeV, and will soon be 
studied at ~i TeV. Electron -pos itron machines, now at 35 GeV, 
will become available at 200 GeV. Electron -proton machines, not 
now available, will be constructed. With these new machines a- 
building, it is clear that many new discoveries will be made 
in the active mode: 

(1) The observation of W and Z. 

(2) The discovery of the top quark, or its replacement in a 
topless theory. 

(3) The revelation of the decay scheme of 6-matter. 

(4) "Direct" observation of the tau neutrino and measurement 
of the tau lifetime. 

(5) Observation of the Higgs boson. 



13 - 



(6) Observation of new hadrons: glueballs, qqqqq or qqqqqq 
states, doubly charmed baryons, the F-meson,. etc. 

(7) Measurement of total cross sections at high energies. 

(8) Discovery of unanticipated new quark and lepton flavors, 
and other surprises. 

Despite the ongoing excitement of the active frontier, 
there is some cause for despair. Most experiments that can be 
done tell us very little about the most fundamental questions. 
The theory points to grand unification at energies of ~i0 14 GeK. 
Accelerators, large as they are, will never get this far.- Ex- 
cept, that is, for the ultimate accelerator-- the universe at 
birth. 

The key to the 10 GeV domain lies in passive experimen- 
tation, of which astronomical observation is a characteristic 
example. Here are some examples of what may be found at the 
passive frontier: 

(1) There are two slim windows into the world of grand unifi- 
cation. One is the possible observation of proton decay. 
The effective four-fermion coupling for this process is sup- 
pressed by the superheavy mass M. We expect 

r p ~ lM/M w ]* r D ^10 a ° years, 

a prediction soon to be tested. 

(2) The second window involves the possibility of neutrino mas- 
ses and neutrino mixing. Again, we expect neutrino masses 
suppressed by the factor iM^/M] with respect to normal mas- 
ses This yields the expected domain 10' eV - 10' eV , which 
is not without its experimental sequelae. 

(3) There may be other types of matter which have not yet been 
observed. I am thinking, for example, of hadrons made up of 
so-called " techniquarks" . 

Such entities may exist in nature. We shall discuss several 
of the ways they may be found. (Also in this category is the 



- 14 - 

usual litany of unobserved stuff: monopoles and quarks). But, 
we shall mostly be concerned with the search for superheavy 
isotopes of conventional chemical elements. 

The passive frontier does involve massive experimental 
devices, although not high energy accelerators. Thus, proton 
decay experiments involve mu lti -kilo ton detectors; the search 
for solar neutrinos will require 50 tons of gallium; neutrino 
oscillations may be found with the aid of power reactors; and 
new heavy matter may be searched for with tandem Van der Graaf 
machines. And,the space telescope will probably cost more than 
any high-energy particle accelerator. 

Our view of particle theory today is totally di fferent than 
ever before. We have what could be called a complete and con- 
sistent theory of low energy (<10 GeV) phenomena. Many of the 
problems of yesterday have been solved. We are left with such 
hard questions as "why are there fermion familes?" or "what 
happens at 10 *GeK?" or "what about gravity?" The familiar par- 
ticle in teractions -- weak, strong and electromagnetic- -are be- 
lieved to result from a spontaneously broken gauge theory. 

The relevant gauge group is generally taken to be 

G = G ^SU(3) x SU(2) x y(l) , 
and its unbroken subgroup is generally taken to be 

H =ff *SU(3)x'U(l)'. 

These particular assignments may be wrong in detail. Pos- 
sibly G > Go while H=H - This would imply the existence of more 
weak intermediaries than the usual W and Z. Georgi and I have 
discussed a number of theories of this kind designed to describe 
a "topless universe", that is to say, wherein there is no top 
quark at all. Some examples we have considered are 

G =SU(3) xSU(2) *SU(2) *U(1) 

G =SU(U) xSU(2) *U(1). 



15 - 



Other possibilities, for other reasons, have been considered 
by other authors. 

Natural topless theories are rife with dramatic predic- 
tions. There are more than just three weak interaction inter- 
mediaries. There must exista fourth charged leptonanda fourth 
Q = -l/3 quark. The bottom quark must decay bizarrely always 
semileptonically and always in.cluding tau or its neutral part- 
ner. The electric dipole moment of the neutron should be large 

_ 2 5 

(~i0 ecm.) rather than the much smaller value expected in more 
conventional theories. 

There is another way in which we may be wrong. It is pos- 
sible that both G> G and H>H . An example is 

G -SV(4) xSU(3) xSU(2) x(j(l) 
H =SU(4) xSU(3) *U(1). 

This is the notion of "technicolor" invented by Susskind 
and others. Dynamical breaking of chiral technicolor is the 
mechanism which establishes the mass scale of the weak coup- 
lings 

G p ~ 200 GeV. 

The possibility that we have misidenti fi ed either G or H 

is one of the reasons that the construction of LEP is essential. 

+ - 
With e e collisions of 250 GeV, we ought to be able to test 

whether or not our theory of the moment is correct in detail. 

However, present experimental data gives us no reason to 
doubt the validity of our assignments G=G Ql H=ff . The simplest 
possibility may be true. We may be stuck with SU(3)xSU(2)x(J( 1) 
all the way up to the unification mass of 10 GeV. 

The strong electroweak gauge group, SU(3) x SU( 2) * U( 1) , 
begs to be unified--to be put into a larger simple group. The 
observed fermions form well defined anomaly -free representations 
of SU(3) x SU( 2) x \}(1). These representations may be extended to 



16 



be representations of a simple group - SU(5) . The extension is 
unique. No other unifying group is possible, unless there exist 
other kinds of fermions which are presently missing from our 
list. 

In a unified theory, the strong and electromagnetic coup- 
ling constants are equal. The observed disparity in strength 
must be a renormali zation group effect, and it determines the 
energy at which the unified symmetry appears. From the observed 
strong and electromagnetic couplings we may deduce: 

(1) The unification mass ~3 x lO^^GeV- 

3 1 ^2 

(2) The proton lifetime ~10 years 

(3) The value sin*d w ^'0.2. 

Thus the three central predictions of grand unification: 
The correct value of the weak mixing angle has been confirmed 
by experiment. Only the desert and the death of matter await 
us. 

Grand unification explains a lot. It tells us why QCD is 
a stronger force than QED. It treats leptons and quarks as mem- 
bers of the same multiplets-- lepton-quark simmetry is under- 
stood. It enforces quantization of electric charge, and ensures 
that colored particles have appropriate fractional charges. It 
suggests that all symmetry is gauge symmetry, and lets us ex- 
punge the ugly global symmetries from the theory. 

In SU{5) .protons and all nuclear matter eventually decay. 
The famous and quite mysterious law of conservation of baryon 
number is lost. This should be thought of as good news, not bad 
news. Who wants ugly global symmetries? Surely the only good 
symmetry is a gauge symmetry. Everything should be allowed that 
is not explicitly forbidden. 

In SU(5), when it is simply implemented, not all global 
symmetry is lost. The selection rule A6 =AL survives. Thus, the 
proton may decay into a positron or a positive muon , but not 
into negative lepton. Majorana masses of the neutrinos, which 



17 - 



transform as AL = 2 , are likewise forbidden at this stage. This 
is a somewhat unsatisfying picture, for if we are to do away 
with global symmetry, we should do away with all global sym- 
metry. 

Even in this "conventional" picture of proton decay, there 
is much to be learned by experiment. The decay modes are 

Nucleon -• Meson (s) + Antilepton, 

and there are six empi rical possibi li ties depending upon whether 
the meson state is S - or S = 1 . (5 =-1 meson states are ac- 
cessible only by effective six-fermion weak interactions). The 
final state lepton may be /J. , e or an antineutrino.lt will be 
of the greatest importance to determine the branching ratios 
among these modes. Moreover, we must learn the Lorentz struc- 
ture of the four-fermion coupling responsible for each of the 
decays. A whole new class of fermion couplings must be studied- - 
i t is the story of the weak interactions revisited. 

It is also possible that naive SU(5) is too naive. The pro- 
ton may decay in other ways. The theory can easily be modified 
to expunge all global symmetry; and to predict AB = -At as well 
as AB=AL. Then, we would expect to see decays into negative 
leptons (like N -*tt e )as well as positive leptons (like N ~"rr~ e ) . 
Not only is this another experimental challenge, but it sug- 
gests the possibility of other intriguing phenomena. AL = 2 in- 
teractions are essential if neutrinos are to develop Maj orana 
masses and to measurably perform their dance of identity. Such 
interactions are expected in a theory which violates all global 
symmetries. They appear quite naturally, for example, in unified 
theories based on 0(10). 

Another bit of exotica is the possibility of AS = 2 inter- 
actions. These may arise as effective six-fermion couplings, 
and are expected to be prepos terou'sly small in any known model. 
But, this is hardly a good reason not to look for such coup- 
lings. Experimenters have too often been led astray by theorists. 



- 18 



Neutral currents could have been found in the sixties. 

AB = 2 interactions lead to two kinds of observable effect. 
In second order, they yield AB = 2 nuclear decays. The Reines 
limit on AB = 1 applies just as well to AB = 2 decays like 

+ + - o 

n + p ~*TT TT TT 7T . 
— 1 29 

Thus, we conclude " (AB=2) > 10 y. The next generation 
of experiments may reveal AB =2 or set a limit 1000 times more 
stringent. Certainly, the AB =2 decay with an energy release 
of 2 GeV will be a conspicuous event if it occurs at all. 

The second effect is an induced transition between neutrons 
and antineu trons, which takes place at first order in the AB =2 
interaction. For the characteristic time T of such N - N oscil- 
lations we obtain the limit 

T> \T(£B*2) tyy]" 1 ^10° s. 

If large numbers of slow neutrons can be kept in magnetic 
isolation for a significant time, a much better limit on T can 
be established. Or, n - n transitions may be observed. It seems 
technically feasible to improve the limit on T by at least two 
orders of magnitude. 

Another important passive experiment concerns neutrino 
masses and neutrino oscillations. These will be dealt with at 
length at this conference. A few declarative sentences on this 
subject ought to suffice. 

(1) In unified theories, neutrinos often do acquire masses and 

-2 - 6 

mix. Masses of 10 -10 eV appear naturally, although 
larger values cannot be excluded. We cannot estimate what 
the leptonic analogs to the Cabibbo angle should be. 

(2) Present "limits" on the size of neutrino oscillations are 
fuzzy. They seem to indicate- -fuzzi ly - -that there are neu- 
trino oscillations. The solar neutrino experiment - -taken 



19 - 



too lit.erally --says that there is maximal mixing, when the 
experiment is sensitive to masses as small as. 10 eV . Reac- 
tor experiments suggest effects. Beam dump experiments sug- 
gest effects. All these experiments must be (and are being) 
repeated with greater precision. 

(3) The observation of nonvanishing neutrino masses and mixings 
will be a great boon to the theorist. With the masses of 
five quarks and three leptons in hand,, we cannot predict 
the mass of the missing top quark. As things are, we know 
not' what we do. We need more hints. 

(4) Reactors and beam dumps are sensitive only to neutrino mas- 
ses larger than ~0. 3 eV. Solar neutrino experiments suffer 
from several astrophysical and nuclear uncertainties. How 
convenient it is that the upcoming generation of proton de- 
cay experiments will suffer from a "background" of order 
~1000 neutrino events per year. A study of this background 
is sensitive to neutrino masses of order 0.003 eV . One way 
or the other, observable neutrino oscillations may be es- 
tablished within the next several years. 

Can there exist new forms of matter on earth which have 
not yet been detected? First, let us consider new forms of stable 
matter. Such things are predicted in certain theories involving 
yet unobserved exact gauge symmetries. Suppose, for example, 
there were an unbroken SU(5) symmetry. "Baryons" could bebuilt 
up out of five "techni quarks". These could not decay to ordinary 
fermions via four-fermion interactions , but would have to decay 
at second-order if at all. It is reasonable to beli eve that such 
particles would have lifetimes longer than ordinary baryons-- 
th.ey are essentially stable. 

We cannot estimate how much of this matter should exist 
today--this depends too much on the detailed properties of the 
new matter and on the nature' of the big bang. We have no idea 
where it is most likely to be found today, just as we have no 
idea where to find gold. Nonetheless, it is worth looking. 



20 - 



Suppose the X -matter is singly charged and has a mass be- 
tween 100 GeV and 100 TeV. The X' would find itself bound to 
common nuclei, and would mimic a superheavy isotope of Z one 
less. We must search for heavy isotopes of B, N, Al, Mn , etc. 
An X without nuclear interactions should mimic a superheavy H 
isotope; with nuclear interactions it might prefer to end up as 
X H g , which acts like superheavy Li. 

The experimental protocol is simple. 

(1) Guess a plausible source (river effluvia, oyster shells, 
manganese nodules, meteorites, etc.). 

(2) Concentrate the putative superheavy isotope by centrifuga- 
tion . 

(3) Search for discrete low values of e/M in a tandem Van der 
Graaf, with a foil to disrupt molecular or polymeric sys- 
tems. Such searches have been done for low mass systems 
(<100 A MU ) , but never to my knowledge for such heavier 
systems as may be expected. 

The new matter mightbeunstable.lt might still be around, 
but decaying: or it might have decayed at an earlier epoch in 
the universe. In any case, there are serious bounds on the con- 
centration of such superheavy particles. They could have been 
detected by their decay products. 

Paul Frampton and I have worked out the limits that now 
exist on the concentration of heavy unstable matter, and the 
improved limits that may result from future experiments. We as- 
sume that the decay products of X include either muons or neu- 
trinos. These secondaries can be detected in massive underground 
detectors. At present, there seems to be no evidence for the 
existence of such secondari es . Current and future limits on the 
existence of such particles with masses of 300 GeV -30 TeV and 

5 3 

lifetimes 10 - 10 years are shown in the figure 1. 

Let me summarize my introductory talk with a brief list 
of the exciting phenomena which may lie on the passive front ier. 
All are fraught with deep cosmological significance. All are 



- 21 



consistent with the view that accelerator physics, though far 
from dead, is approaching that great desert in which the only 
surprise is desolation. 



E-ITeV (M~3TeV) 




lo| Y$ 1C^ W W lOfr 



Figure 1 

Plot of concentration C against lifetime T for E=l TeV (cor- 
responding to mass "~ 3TeV) . Shown are the present bound (solid 
line) and the bound (broken curve) accessible to the new pro- 
ton decay experiments. In this plot, the existing bound is from 
endogenous muons (T>6xlCTy) and from secondary anions pro- 
duced by relic neutrinos (T<6xl0 y). The new bound is from 
endogenous muons {T>6X10 y) , from secondary muons produced 

7 8 

by relic neutrinos (/ '4x10 y<T<6xlO y) and from direct 
detection of relic neutrinos (T < 1 • ix 10 y) . Also shown by 
"windows are portions of the curves corresponding to E = 100 GeV 
(M^-300 GeV) and E * 1 TeV {M ^30 TeV). (From P. Frampton and 
S. Glashow, Harvard preprint HUTP-80/A007 ) . 



22 



Proton Decay 

Neutrino Oscillations 

Neutron -Antineutron Oscillations 

Superheavy Isotopes 

Neutrino Events From Astrophysical Catastrophes 

Violation Of Charge Conservation 



Only if none of these phenomena show up, and if the desert 
is as bleak as some expect will Eddington's prophecy be ful- 
filled: that physics will have become complete, and hence un- 
interesting. As things are now, all we can say (and this for 
the first time) is that our discipline is at risk. 



23 



-1.25 




Re 15' 



SENSITIVITY OF 
FIRST GENERATION 
EXPERIMENT 



-0.75 



O50 



Figure 2 

Neutrino mixing effects in deep underground experiments. R 
signifies the ratio of upward-directed to downward -directed 
neutrino events with a muon . R signifies the same ratio for 
events with an electron -It is assumed that the downward flux 
is unmixed and involves twice as many muon neutrinos as elec- 
tron neutrinos. The allowed region is shown. The origin cor- 
responds to no mixing. The result to a hypothetical first 
generation is shown. The smaller region corresponds to the 
constraint that no neutrino' mixing angle exceeds the Cabibbo 
angle. 



25 - 



JOHN N. BAHCALL ( * ) 



SOLAR NEUTRINOS 



The topics I will cover aTe, in order: an overview of the 
subject of solar neutrinos, a brief summary of the theory of 
stellar evolution, a description of the main sources of solar 
neutrinos, a brief summary of the results of the Brookhaven 37 Cl 
experiment , an analysis of the principal new solar neutrino ex- 
periments that have been proposed, a discussion of how solar 
neutrino experiments can be used to detect the collapse of stars 
in the Galaxy, and finally, a description of how the proposed 

7 1. 

Go experiment can be used to test for charge non -conservation . 
Most of the information contained in this talk has been sum- 
marized in recent reviews [l ,2 , 3 ,4 , 5] . 

The most important fact about the subject I am reviewing 
is that there is a serious discrepancy between the standard 
theory and observation. 

One may well ask: Why devote so much effort in trying to 
understand a backyard problem like the sun's thermonuclear fur- 
nace when there are so many exciting and exotic discoveries oc- 
curring in astronomy? Most natural scientists believe that we 
understand the process by which the sun's heat is produced - 
that is, in thermonuclear reactions that fuse light elements 
into heavier ones, thus converting mass into energy. However, 
no one has found an easy way to test the extent of our under- 
standing because the sun's thermonuclear furnace is deep in the 
interior, where it is hidden by an enormous mass of cooler ma- 
terial. Hence conventional astronomical instruments can only 



(*) School of Natural Sciences -The Institute for Advanced Study -PRINCETON, 
N.J. 08540. 



- 26 



record the photons emitted by the outermost layers of the sun 
(and other stars) .The theory of solar energy generation is suf- 
ficiently important to the general understanding of stellar 
evolution that one would like to find a more definitive test. 

There is a way to directly and quantitatively test the 
theory of nuclear energy generation in stars like the sun. Of 
the particles released by the assumed thermonuclear reactions 
in the solar interior, only one has the ability to penetrate 
from the center of the sun to the surface and escape into space: 
the neutrino. Thus neutrinos offer us a unique possibility of 
"looking" into the solar interior* Moreover, the theory of 
stellar aging by thermonuclear burning is widely used in inter- 
preting many kinds of astronomical information and is a necess- 
ary link in establishing such basic data as the ages of the 
stars and the abundances of the elements. The parameters of the 
sun (its age, mass, luminosity, and chemical composition) are 
better known than those of any other star, and it is in the 
simplest and best understood stage of stellar evolution, the 
quiescent main sequence stage. Thus an experiment designed to 
capture neutrinos produced by solar thermonuclear reactions is 
a crucial one for the theory of stellar evolution. We also hoped 
originally that the application of a new observing technique 
would provide added insight and detailed information.lt is for 
all of these reasons (a unique opportunity to see inside a star, 
a well-posed prediction of a widely used theory, and the hope 
for new insights) that so much effort has been devoted to the 
solar neutrino problem. 

A number of exotic solutions to the solar neutrino prob- 
lem , modi fying either the physics or the astronomy (and in some 
cases both), have been proposed. Even if one grants that the 
source of the discrepancy is astronomical, there is no general 
agreement as to what aspect of the theory is most likely to be 
incorrect. As indicated above, many of the proposed solutions 
of the solar neutrino problem have broad implications for con- 



27 



ventional astronomy and cosmology. Some of them would change 
the theoretical ages of old stars or the inferred primordial 
element abundances. On the other hand, modi fied theories of the 
weak interactions have been proposed in which neutrinos may dis- 
appear by mixing or decay in transit from the sun to the earth, 
but for which there are no terrestrially measurable conse- 
quences. It is conceivable tha.t one of these modified theories 
of the weak interactions is correct and the standard solar mo- 
del is not in conflict with observations. 



STELLAR EVOLUTION 

I have listed on Table 1 everything that I think you need 
to know about stellar evolution. There are many more things in 
stellar evolution theory, but I don't think you have to know 
them in order to understand solar neutrino experiments, cer- 
tainly not for the purposes of this talk. Table 1 summarizes 
the principles that are required for constructing solar models 
and that are tested by solar neutrino experiments. 

The first principle is hydrostatic equilibrium, which in 
practice is used together with the special assumption of spher- 
ical symmetry. The second principle is that the energy source 

TABLE 1 
Three minute course in Stellar Evolution Principl e s 

Hydrostatic Equilibrium 

Spherical Sun 

Nuclear Energy Source 

Energy Transport by Radiation & Convection 

Uniform Primordial Composition = Surface Composition 

9 
Evolution (age =5x10 yrs'. ) 

37 
BOTTOM LINE: Only CI Experiment Inconsistent with 

Standard Theory 



28 



is postulated to be nuclear; the rates of the nuclear reactions 
depend on the density (p) and the temperature (D.and the com- 
position (X .) . The practical part of this principle is that the 
rate at which the nuclear reactions produce energy when inte- 
grated over the whole sun is equal to the observed solar lumi- 
nosity today. The "today" is an essential part of this prin- 
ciple. 

The third principle is that the energy is transported from 
the deep interior to the surface via radiation and convection. 
In practice, for most (but not quite all) of the models, the 
great bulk of the energy is transported by radiation. The key 
quantities are the gradient of the temperature (dT/dr) and the 
opacity of the solar matter. 

The assumption that the initial composition was uniform 
and is equal to the presently observed surface composition is 
closely related to the question of which opacity should be used. 
It is plausible that the surface composition has not changed 
much because of nuclear reactions since the sun was formed. It 
is not quite so obvious that nothing has been added to the solar 
surface since the sun was born. However, that is the assumption 
which is widely used throughout astronomy and is the basis for 
making the standard calculations. 

The final principle is that the sun evolves because it 
burns its nuclear fuel. It has burned for something like 5 bil- 
lion years so far. One mocks up this evolution by computing 
several quasistatic models which march along in time. 

The bottom line of this brief course in stellar evolution 
is: within our store of observational information about stars, 
only the Brookhaven Chlorine 37 experiment of Ray Davis and his 
colleagues is inconsistent with the standard theory of stellar 
evolution. It is the only place where we don't see' a way out 
of observational difficulties unless we modify something among 
the basic assumptions. 



29 - 



NUCLEAR FUSION IN THE SUN 

I shall now outline briefly the conventional wisdom [5,6,7] 
regarding nuclear fusion as the energy source for main sequence 
stars like the sun. It is assumed that the sun shines because 
of fusion reactions simi lar to those envisioned for terrestrial 
fusion reactors. The basic solar process is the fusion of four 
protons to form an alpha particle, two positrons (e + ), and two 
neutrinos (v) , that is, hp -a+2e + +2v e . The principal reactions 
are shown in Table 2 with a column indicating in what percentage 
of the solar terminations of the pro ton -pro ton chain each reac- 
tion occurs. The rate for the initiating proton -pro ton (PP) 
reaction, number 1 in Table 2, is largely determined by the 



TABLE 2 
The proton-proton chain in the sun 







Solar 




Number 


Reaction 


terminations 


Maximum Neutrino Energy 






(%) 


WeV) 


1 


2 + 
p +p " H + e +V 

or 

2 

p + e + p — H +V 


(99.75) 


0.420 


2 


(0.25) 


1.44 (monoenerget ic ) 


3 


2 3 
H +p - He +V 


(100) 




4 


3 3 4 

He + He - He + 2p 


(86) 




5 


or 

3 4 7 

He + He - Be +V 


(14) 




6 


7 _ 7 

Be + e — Li +v 




0.861 (90%), 0.383 (10%) 


7 


1 '. * 
Li +p -2 ffe 




(Both monoenerge tic) 


8 


or 

7 8 

Be +p — B +v 


(0.02) 




9 


8 8.+ 

B- Be + e +V 




14.06 


10 


B«*-2 ffe 







- 30 - 
total luminosity of the sun. Unfortunately , these neutrinos are 

3 7 

below the th reshold, which is 0.81 MeV, for the CI experiment. 
Several of the proposed new experiments, especially the Ga 
experiment [8], will be primarily sensitive to neutrinos for 
the p-p reaction. The PEP reaction (number 2 ) .which is the same 
as the familiar PP reaction except for having the electron in 

3 7 

the initial state, is detectable in the CI experiment. The 
ratio of PEP to PP neutrinos is approximately independent of 
which model (see below) one uses for the solar properties. Two 
other reactions in Table 2 are of special interest. The capture 
of electrons by Be (reaction 6) produces detectable neutrinos 
in the CI experiment. (Just recently, I have had a lot of fun 
calculating the rate at which Be neutrinos from the sun induce 
the terrestrial reaction: v so i ar + Be-' Li +e~. There are some 
amusing considerations in this set of reactions: for example, 
if you take account of terrestrial electron screening but fail 
to include the thermal width of the ions and electrons in the 
sun, you incorrectly obtain an answer of zero Llj). The B beta 
decay, reaction 9, was expected to be the main source of neu- 
trinos for the CI experiment because of their relatively high 
energy (14 MeV) , although it is a rare reaction in the sun (see 
Table 2). There are also some less important neutrino-producing 
reactions from the carbon -nitrogen -oxygen (CNO) cycle, but we 
shall not discuss them in detail since the CNO cycle is believed 
to play a rather small role in the energy -production budget of 
the sun. 



THE BROOKHAVEN SOLAR NEUTRINO EXPERIMENT 

The Brookhaven solar neutrino detector is based on the 
neutrino capture reaction [2,3,4,9] . 

capture 
v + 37 Cl , 3? Ar+e" (1) 

decay 



- 31 - 

which is the inverse of the electron capture decay of 37 Ar. The 
radioactive decay occurs with a half-life of 35 .days. This re- 
action was chosen for the Brookhaven solar neutrino experiment 
because of its unique combination of physical and chemical 
characteristics, which were favorable for building a large- 
scale solar neutrino detector .Neutrino capture to form ° 7 Ar in 
the ground state has a relatively low energy threshold (0.81 Mev) 
and a favorable cross section, nuclear properties that are im- 
portant for observing neutrinos from 7 Be , 13 N, and 15 decay 
and the PEP reaction. 

_ 3 7 

The CI reaction is very favorable from a chemical point 
of view [2 ,4,9, 10] .Chlorine is abundant and inexpensive enough 
that one can afford the many hundreds of tons needed to observe 
solar neutrinos. The most suitable chemical compound is per- 
chloroethylene, C 2 Cl 4 , a pure liquid, which is manufactured on 
a large scale for cleaning clothes. The product, 37 Ar, i s a noble 
gas, which should ultimately exist in the liquid as dissolved 
atoms. The neutrino capture process produces an Ar atom with 
sufficient recoil energy to break free of the parent perchlor- 
ethylene molecule and penetrate the surrounding liquid, where 
it reaches thermal equilibrium. 

3 7 

The Brookhaven CI detector was built by Davi s deep under- 
ground to avoid the production of Ar in the detector by cos- 
mic rays. This was done with the cooperation of the Homestake 
Gold Mining Company (Lead, South Dakota), who excavated a large 
cavity in their mine (~1500 m below the surface) to house the 
experiment. The final detector system consists of an ~400,000 
liter tank of perchloroethy lene , a pair of pumps to circulate 
helium through the liquid, and a small building to house the 
extraction equipment. 

A set of 39 experimental runs carried out in the Brook- 

3 7 

haven CI experiment over the last 10 years show that the 37 Ar 
production rate in the tank is 0.50 ±0.06 3? Ar atoms per day 
[2,3] . Even though the tank is nearly a mile underground, a 

3 7 

small amount of Ar is produced by cosmic rays. An evaluation 



32 



of data obtained by exposing 7500 liters of C 2 Cl^ at various 
depths underground suggests that the cosmic-ray production rate 

3 7 r t 

in the detector may be 0.08 ±0.03 Ar atoms per day L2.3J. 

3 7 

Fireman's [ll] measurements of the muon background using a K 

3 7 

detector suggest a background rate of (0. 18 ± 0.09) Ar atoms/ 
day. If this background rate is correct then there is no evi- 
dence for any solar neutrino detect ion beyond the 3-cr level of 
s ignificance . 

If the background rate determined from the C 2 CI 4 measure- 
ments is assumed, then a positive signal of (2.2 ±0.4) SNU is 
inferred [2,3,4] (1SNU = 10' captures per target particle per 
second) . 

The predicted capture rates for one recently constructed 
solar model are shown in Table 3 L5] . The results are expressed 
in terms of SNU' s =10' captures per target atom per second, 
the characteristic coun ting rate for solar neutrino experiments. 
The neutrino absorption cross sections used to compute the rates 
given in Table 3 are from reference [ll .The best values to use 
for various nuclear parameters is currently under investigation 
and the total predicted rate may well differ by as much as 1 to 
1.5 SNU from the value of 7.5 SNU shown in Table 3. 



TABLE 3 
Predicted Capture Rates for a Recently Computed Solar Model 



Neutrino Source 


Capture Rate 
(SNU's) 


P-P 





e 
B 


6 


PEP 


0.2 


7 

Be 


1 


13 

N 


0.06 


15 




0.2 


Total = 


7.5 SNU 



33 



OBSERVATIONAL IMPLICATIONS 



The CI experiment tests theoretical ideas at different 
levels of meaning, depending on the counting rate being dis- 
cussed. The various counting rates and their significance are 
summarized in Table 4. It is obvious from a comparison of Table 
4 with the experimental results given above that the value of 
28 SNU' s based on the CNO cycle is ruled out. More surprising- 
ly, the best current models based on standard theory, which 
imply ~6 to 8 SNU' s are also inconsistent with the observations . 
This disagreement between standard theory and observation has 
led to many speculative suggestions of what might be wrong. One 
such suggestion [l2],that in the solar interior the heavy ele- 
ment abundance is at least a factor of 10 less than the observ- 
ed surface abundance, leads to an expected counting rate of 
1.5 SNU' s (see Table 3), which is about as low a prediction as 
one can obtain from solar models without seriously changing cur- 
rent ideas about the physics of the solar interior. We note that 

■ 3 7 

present and future versions of the CI experiment are not like- 
ly to reach a sensitivity as low as 0.3 SNU, the minimum count- 
ing rate (from reaction 2 of Table 2) that can be expected if 



TABLE 4 
Significance of counting rates in the 



CI 



exper men t. 



One solar neutrino unit (SNU) = 10 captures per target per second 



Counting Rate 
{SNU) 


Significance of counting rate 


28 

7±1 
1.5 

0.3 


Expected if the CNO cycle produces the solar 
luminosity 

Prediction of current models 

Expected as a lower limit consistent with 
standard ideas of stellar evolution 

Expected from the PEP reaction, hence a test 
of the basic idea of nuclear fusion as the 
energy source for main sequence stars 



34 



the basic idea of nuclear fusion as the energy source for main 
sequence stars is correct. 



NEW EXPERIMENTS 

Another experiment is required to settle the issue of 
whether our astronomy or our physics is at fault. Fortunately, 
one can make a testable di stinction . The flux of low energy neu- 
trinos from the PP and PEP reactions (numbers 1 and 2 in Table 
2) is almost entirely independent of astronomical uncertainties 
and can be calculated from the observed solar luminosity, pro- 
vided only that the basic physical ideas of nuclear fusion as 
the energy source for the sun and of stable neutrinos are cor- 
rect. If these low energy solar neutrinos are detected in a 
future experiment, we will know that the present crisis is 
caused by a lack of astronomical understanding. If the low en- 
ergy neutrinos are absent, we will know that the present dis- 
crepancy between theory and observation is due at least in part 
to faulty physics, not just poorly understood astrophysics. 

I have recently analyzed in detail the theoretical aspects 
of eleven experiments that have been studied by various experi- 
mental groups as possible new solar neutrino experiments LlJ . 
Those eleven proposed targets are listed in the first column 
of Table 5. I also list in the other columns the following in- 
formation: (a) whether the total cross -section solar neutrinos 
can be calculated to an accuracy of at least ten percent; 
(6) whether something new will be learned about the solar in- 
terior, or neutrino physics, by performing the proposed experi- 
ment; and (c) whether (in my opinion) the experiment is feasible 
with current technology. A check mark (v) indicates that the 
answer to the relevant question is affirmative; a negative 
answer is indicated by an X. 

The detectors for solar neutrinos can be classified accord- 
ing to their relative sensitivity to different parts of the 



- 35 - 

TABLE 5 
P roposed Experiments 



Ta r ge t 


Cross -Section 


New 


Feasible 


2 

H 


• 


?* 


/ 


7 

Li 


/ 


/ 


y (?) 


37 ci 


• 


/ 


/ 


61 v 


X 


* 


/ 


56 

Mn 


X 


* 


• 


71 

Go 


/ 


/ 


/ 


81 

Br 


* 


/ 


/ 


87 

Rb 


• 


/ 


X (?) 


115 

In 


/ (?) 


/ 


J (?) 


2 ° 5 n 


j 


/ 


S (?) 


v .-'\ 


v/ (f-S) 


?* 


? 


New if <p ( B) ~ 6x 10 c» se 


- l 
c measura 


ble 



solar neutrino spectrum. Five of the experiments are primarily 
sensitive to B neutrinos; these are H, CI, V, Mn , and 
neutrino -elec tron scattering. 

r. , 71 ^t 8 7 r>i 115 t , 205m, 

tour detectors, da Ho In and 11, are primari- 

ly sensitive to neutrinos from the proton -proton reactions. The 
expected capture rates for these de tectors are practically in- 
dependent of the astronomical assumptions that are made pro- 
vided only that the sun produces, in a steady-state fashion and 
via the proton-proton chain, the energy that it radiates from 
its surface. 

The pep neutrinos (reaction 2, Table 2) are expected to 

make the largest single contribution to the capture rate of a 

Li detector, even for the standard solar model. The observa- 

3 7 

tional results from the CI experiment show, moreover, that the 

8 7 

higher energy B neutrinos should con tribute , for a Li target, 
at most one-half the. capture rate due to pep neutrinos. Since 



36 



the pep neutrinos are as good a measure of the proton -proton 
reaction rate as are the p-p neutrinos, one can also classify 
the Li detector as a p-p sensitive target. The Li and In 

targets share the property of being reasonably sensitive to more 
than one neutrino branch (the pep, Be, B, and branches 
for the Li detector; the p-p and Be branches for the In 

target). The p-p and Be capture rates could be determined se- 
ll 5 
parately for the In experiment since the energies of the in- 

dividual electrons could be measured. 

The Br detector is primari ly sensitive to Be neutrinos. 

115 

The In and neutrino -el ectron scattering experiments 

could in principle be used to measure the direction of the elec- 
trons that are produced and thus to establish that the incident 
neutrinos come from the sun. 

In, order for a solar neutrino experiment to be most use- 
ful, the absorption cross sections must be accurately known. 

2 7 7 1 

Of the new targets discussed in this paper, only H, Li, Ga, 

8 7 3. 3. 5 ' 

Rb , In, and neutrino -electron scattering satisfy this re- 

quirement. A new detector should also help disciiminate between 
the possible expl anation s of the discrepancy between theory and 

3 7 2 

observation in the CI experiment . Experiments with H or neu- 

1 • • • • • 1 8 r> 

trino-elec tron scattering are sensitive primarily to B neu- 

3 7 

trinos, as is the CI experiment. In order to provide new in- 
formation of ast rophy si cal importance, these experiments must 
be sensitive to a 6 flux that is significantly below that al - 

3 7 

ready reached by the Brookhaven CI experiment. There has not 
been a recent and detailed experimental feasibility study for 
the proposed Rb experiment , perhaps because of the uncomfort- 

i 8 7 

ably short lifetime (2.8 nrs ) of the daughter nucleus, Sr . If 
we set aside Rb because of the absence of a feasibility study, 

7 7 1115 2 

then the preferred targets are: Li, Ga , In, and either H 

or electron scattering (if sufficiently sensitive). 

There are four major neutrino branches that must be meas- 
ured in order to carry out a program of neutrino spectroscopy 



- 37 - 

_ 7 8 

of the solar in terior. These branches are the p-p, Be, B, and 
N+ neutrinos. The future experimental so lar. neutrino prog- 
ram should include all of the preferred new detectors. The Ga 

3 7 

experiment is primarily sensitive to p-p neutrinos and the CI 

8_ . .m 7 r i 115 t 

experiment to B neutrinos. The Li and In experiments pro- 

vide additional information about the Be and N + fluxes. 

7 3 7 

Taken together, the results of .the four experiments {Li, CI, 

Ga, and In) should allow us to solve for the parameters 

of the solar interior (temperature range, density and composi - 

2 
tion). An H or an electron -neutrino experiment should also be 

performed at some future date in order to check on the upper 
limit to the B flux determined by the CI experiment. If a 
feasible experiment is proposed in which a B flux as low as 
twenty percent of the prediction from the standard model could 
be measured then this would also be a pre f erred experimen t since 
it would provide qualitatively new ast rophy sical information. 

Either a Ga or an In experiment can ' distinguish be- 

tween- explanations that are based on presumed inadequacies in, 
respectively, the astronomical theory or the weak interaction 
theory provided only that the sun produces in a steady-state 
fashion the energy it radiates from its surface. A low counting 
rate in either of these experiments could also arise, in prin- 
ciple, if the sun is now in an abnormal phase in which its nu- 
clear energy generation is much less than its surface luminos- 
ity. However, for most of the models of this kind that have ap- 
peared in the literature, the reduction in the counting rate 

. 71. lie. . , , . n 

of a Ga or an In experiment would not be nearly as great 

as is expected on either the oscillation or the decay hypoth- 
esis. Moreover, these latter two processes lead to specific 
predictions for the Ga and In experiments when combined 

with the results of the CI experiment. 



38 



TESTS OF THE CONSERVATION OF ELECTRIC CHARGE 

The conservation of electric charge is widely believed to 
be an absolute conservation law, valid to anarbitrary accuracy. 
The validity of this law, like all the laws of physics, ulti- 
mately rests upon experiment .There are several very useful dis- 
cussions of experimental tests of charge conservation [13 , 14J . 
The most stringent lower limits on the lifetime of the electron 
( concei vab le decays are, e.g., e -*y +v , e ->2v + v , etc.) are 
of order 10 [22] years for electrons in iodine and germanium 
atoms [l5,16J.The most stringent limit on a nuclear decay (in- 
volving, eg., n-*p +y or n—/3+v c +v e ) with whi ch I am familiar 
is the lower limit of the order of 10 [16] yr on the spontaneous 
decay of 87 Rb to B7 Sr m [17] . 

The discussion here is based on reference one. 

The validity of charge conservation in reactions involving 
nucleons is not guaranteed by experiments that demonstrate the 
stability of the electron. In princi pie, there could be a reac- 
tion which permi tted, at a certain level, n -* p + y or n -* p + v + v 
while forbidding, to the same order of small quantities, all 
decays of the electron. Moreover, the lifetimes for nucleon de- 
cays (n -*p + anything) that are accessible to solar neutrino ex- 
periments are much longer than the limits obtained so far on 
the lifetime of the electron, primarily because of the much 
larger amounts of material and the longer counting times that 
are involved in solar neutrino experimen ts . The nuclear experi- 
ments on charge conservation can provide strin gent , independent 
tests of charge conservation. 

Solar neutrino radiochemical experiments that involve tar- 
gets for which the neutrino capture threshold is less than the 
mass of the electron provide sensitive tests of charge conser- 
vation with no extra effort. Some examples of the kinds of pro- 
cesses that are forbidden by charge conservation but are al- 
lowed by energy conservation and all the other known laws of 
physics are: Ga - Ge + v + j7 and Go.-* Ge + y (E ~275 keV). 



- 39 - 

Targets composed of SS Un, 81 JSr, 87 Rb, and 206 n are also suit- 
able in principle, for tests of charge conservation. 115 Jn can- 
not be used for experiments to test charge non-conservation 
since there is no practical way of detecting sufficiently small 
quantities of the stable product 1±S Sn. Solar neutrino experi- 
ments with In are feasible only because electrons produced 
by neutrino capture (but not by a hypothetical charge noncon- 
serving reaction) are counted- 

The great sensitivity of solar neutrino experiments to 
charge nonconservation can be seen immediately from the defi- 
nition of a SNU, i.e., 10~ daughter atoms produced per target 
atom per second. Translated into lifetimes measurable in a 

radiochemical experiment designed to detect v + A- - e ~ + A .-^ , , , 

e £. [ z + 1 ) 

this gives: 

_/j a , ■ > ^ 2. 2 x 10 year 
t(A z ~A (z+1) + anything) > p (SNU) (2) 

Here P(SNU) is the measured production rate in SNU' s of 
daughter atoms '^(z-n) which, in principle, could be due either 
to solar neutrino captures, to background processes, or to charge 
nonconservation. Note that radiochemical experiments are sen- 
sitive to any mode by which the charge nonconservation is ef- 
fected; this is indicated by the appearance of the word "any- 
thing" in Eq. (2). If the p-p solar neutrinos reach the earth, 
then the ultimate sensitivity to charge nonconservation obtain- 
able with a Ga experiment alone, P ~40 2 , will be a lifetime 

28-8 

~10 years. This is eleven orders of magnitude longer than 

the upper limit obtained in the nuclear decay of a? Rb and B7 Sr 
and four orders of magnitude longer than the most stringent li- 
mits on the lifetime of the electron (to specific decay modes). 
The interpretation of charge nonconservation experiments 
requires some theoretical assumptions. A reasonably general, and 
perhaps plausible, assumption is that the interaction matrix 
element factors into a nuclear part times something else. The 



40 



nuclear part itself can be factored (for the relevent low mo- 
mentum transfers) into an ordinary nuclear beta-decay matrix 
element (obtainable, e.g., from the electron capture rate of 
Ge for a Ga target) times a charge nonconserving nuclear 
matrix element, <n\H \p>. Using Fermi's golden rule with the 
above assumption one can write 



\<n\H \p>\ 2 p=Cln2 A/ 277) (r JQ))' 1 [ftJ6 x 10%] , 



(3) 



where p is the phase space for the decay (which depends on the 
decay mode and theory assumed), and ^y(Q) is the lifetime, or 
upper limit to the lifetime, for charge nonconserving decays 
(cf. Eq. (2)). The nuclear /t^ factor that appears in Eq. (3) 
must be corrected for the statistical factor, [(21+1)/ (21' +1)] , 
that takes account of the difference in spin between initial 
and final nuclear states. For Ga -• Ge , fty^^.6^10 s. In 
the form given in Eq. (3), results of a suitable solar neutrino 
experiment can be interpreted in terms of a limit on a nucleon 
non -charge -conserving matrix element in a manner that is en- 
tirely analogous to, but independent of, the matrix element 
<e"|ff o |0> that is determined by electron decay experiments. 

If one assumes that the weak interactions include a small 
charge nonconserving part that has the usual form except for a 
neutrino replacing the electron in the lepton current, 
H n -sH , , , then one can obtain an interesting limit on 

Q u s aa I Jo rm ' ° 

e. The result may be expressed in terms of the ratio of branch- 
ing ratios for the elementary neutron decays: E =^(n-*p+v g +v e )/ 
rfn-p+e"+v ) . 



Vfn^p+v +v ) 



r( n ->p+ e -+v e ) 



P(SNU)u A (n) 
2.2xl0 +28 yrj 



/ W(n) \ (f f ) A z 
\*(A X )J (ft) n 



(4) 



Here W(n) is the mass difference (1.29 MeV) between a neu- 
tron and a proton; W(A-) is the nuclear mass difference between 



41 



the isotopes A z and A, z+1 y, (ft)A z includes the statistical 
spin factor; and (ft) n = 1. 1 x 10% , t y Jn) =6. 5 x 10* s . For 71 Ga 
one finds 

F(n—p+v +v ) 

6 xlO' 29 P( 71 Ga;SNU). (5) 



r( n -p+e-+v ) 



7 1, 



Thus a Ga solar neutrino experiment will be sensitive to 
a non-charge-conserving part of the weak interactions that is 
more than twenty -six orders of magnitude smaller than the main 
part of the weak interactions. 

There is in principl e some ambiguity in interpreting radio- 
chemical solar neutrino experiments in which the neutrino 
capture threshold is less than the mass of the electron. How 
can one be sure that a measured counting rate in, for example, 
the Ga experiment is due to solar neutrinos instead of charge 
nonconservation? There are two answers to this question: one 
theoretical, one experimental. First, all current theoretical 
considerations suggest that it is much more likely that the p-p 
solar neutrino flux is of the predicted orde r of magnitude than 
that charge is not conserved at a level that accidentally is 
of the right order of magnitude to be detectable in a solar neu- 
trino experiment. Second, the capture rates in the Go and 

115- . 115 

In experiments can be compared. The experiment with Jn is 

• • 7 r> 

sensitive to p-p and Be neutrinos but in the proposed electron 
counting mode cannot detect charge nonconserving transitions 
of In to Sn . If the counting rates in the Ga and In 

experiments are consistent with the same solar neutrino fluxes, 
then the Ga experiment may be interpreted additionally in 
terms of an upper limit on charge nonconserving reactions. Com - 
Dining the ha and In experiments may permit an increase 

by one order of magnitude in the. sensitivity estimated above 
of the Ga experiment to charge nonconservation. 



- 42 - 

ACKNOWLEDGEMENT 
This work supported in part by NSF Contract PHY77 -20612. 

REFERENCES 

[l] BAHCALL J.N. (1978) "Rev. Mod. Phys . " 50, 881. 

[2] DAVIS R. (1978) "Proc. of the Brookhaven Solar Neutrino Conference" 

1,1. 

[3] ROWLEY J.K., CLEVELAND B. T. , DAVIS R. Jr.,HAMPEL W..KIRSTEN T. (1980) 
The Present and Past Neutrino Luminosity of the Sun", BNL preprint 
27190. 

[4] BAHCALL J.N. and DAVIS R. Jr. (1976) "Science" 191, 264. 

[5] BAHCALL J.N. , "Space Science Reviews" 24, 227. 

[6] SCHWARZSCHILD M. , Structure and Evolution of the Stars, Princeton Uni- 
versity Press, Princeton, NJ (1958). 

L7J CLAYTON D.D. , Principles of Stellar Evolution and Nucleosyn thesis , New 
York: McGraw-Hill, 612 pp. (1968). 

[8] BAHCALL J.N. , CLEVELAND B. , DAVIS R. Jr. , DOSTROVSKY I., EVANS J.C.Jr., 
FRATTI W. , FRIEDLANDER G. , LANDE K., ROWLEY K. , STONER D. and WENESER 
J. (1978) "Phys, Rev. Lett." 40, 1351. 

[9] DAVIS R. Jr. (1964) "Phys. Rev. Lett." 12, 303. 

DAVIS R. Jr. (1969) "Proc. Int. Conf. Neutrino Physi6s and Astrophys. 
(Moscow) "2, 99. 

[l0] PONTECORVO B. (1946) Chalk River Lab. Rep. PD-205. 

ALVAREZ L.W. (1949) Univ. Calif. Radiat. Lab. Rep. UCR-328. 

[ll] FIREMAN E.L. (1979) "16th Int. Cos. Ray Conf., Kyoto, Japan" Vol.12. 

[12] BAHCALL J.N. and ULRICH R.K. (1971) "Ap.J." 170, 593. 

[13] FEINBERG G. and GOLDHABER M. (1959) "Proc. Natl. Acud, Sci." USA 45, 
1301. 

[14] GOLDHABER M. (1975) "Proc. Am. Philos. Soc." 119, 24. 

[l5] STEINBERG R.I., KWIATKOWSKI K. , MAENHAUT W. , WALL N.S., (1975) "Phys. 
Rev." D 12, 2582. 

[l6j MOE M.K. and REINES F. (1965) "Phys. Rev." B 140, 992. 

[l7] SUNYAR A.W. and GOLDHABER M. (1960) "Phys. Rev." 120, 871. 



43 



MALVIN RUDERMAN ( * } 
SUPERDENSE MATTER AND ELEMENTARY PARTICLE PHYSICS 



I. INTRODUCTION 



Astrophysics is general ly an al ert consumer of new develop- 
ments in fundamental particle physics. But only rarely is it a 
potential contributor by offering important regimes of physi cal 
parameters not available in the laboratory .Superdense and super- 
hot bulk matter can have important collective or gravita- 
tional effects which do not show up ( easi ly ) in laboratory col- 
lision experiments involving very few particles. Where we find 
such matter and what it may tell us is the main subject of this 



review, 



II. SUPERDENSE MATTER IN THE PRESENT UNIVERSE 

Among the most significant features of superdense (denser 
than nuclear) matter is the almost total absence of any such 
homogeneous fluid filling our present universe. A fluid with a 
stress- energy tensor of the form T^ 'Poc^g^ would be a con- 
sequence of any theory with a Lorentz invariant vacuum energy 
density. Such an energy density might originate from 

a) zero point energies of the elementary quantum fields. 
Just because these are infinite in most theoretical estimates 
does not mean they are necessarily zero. Supersymmetri c the- 
ories encompassing bosons, fermions and gravity can give the 
needed cancellations but the symmetry and presumably the can- 



(*) John Simon Guggenheim Fellow. Research supported in part by a grant fi 
the National Science Foundation. 



44 - 



cellation are clearly not an exact symmetry in our present 
Un i v e r s e . 

6) Expectation values of the energy density of the scalar 
(Higgs) fields condensate whose existence is critical to pre- 
sent symmetry breaking models for the marriage of weak and elec- 
fjajmagnetic interactions and for higher level unification mo- 
de Is . 

In these theories dimensional considerations suggest 
p ~m*c 3 /i~ =(mc /GeV) '10 gem' .where m is amass constructed 
from those of relevant particles and associated coupling con- 
stants. But observations of the expansion velocity to distant 
galaxies give a limit \p \ & 10' gem' . "Cosmological matter" 
of this sort would be manifest as a cosmological constant in 
the Einstein Field equation LI J : 

R „( ma tter) . 

where the last term of the RHS can be interpreted as, at least 

2 

in part, the T of "cosmological matter" for which p=p =-Poc = 
(8n)' 1 A. The energy density contributions from (a) and(b) above 
can, of course, be renormalized to zero by choosing A=0 in eq. 
(1). But just why this is so precisely cancelled in our present 
Universe is still unclear - especially when the exciting big 
bang scenarios which involve phase changes with symmetry break- 
ing in the very early universe must begin wi th a huge A if later 
Higgs condensates are not to result in one [2]. In the absence 
of better arguments one may even consider an anthropic one. In 
a homogeneous isotropic expanding universe the distance between 
galaxies r varies according to 

r = (p+3p)r (2) 

If "cosmological matter" dominates the RHS with p ~p , 
p^-Po, then r^8nGp r/3. Thus a large p > results in strong 



45 



positive acceleration which may not allow enough time after the 
radiation-matter decoupling to permit galaxies to condense, 
stars to form, and, most important, astrophysicist observers to 
evolve, before matter becomes too dilute to support the needed 
condensations. If, on the other hand, p is large but negative 
the expansion of the universe would long ago have reversed and 
resulted in a big "crunch" before observers could be evolved. 

Any evidence at all for a non -vani shing A in Eq. (5) may 
turn out to be of interest in understanding the possible rela- 
tionships among elementary particle theories, especially those 
which have symmetry breaking condensates , and gravitational ef- 
fects of the resulting "cosmologi cal matter". Such evidence may 
come from a comparison of the Hubble constant which gives the 
present expansion rate of the Universe and other evidence for 
the minimum age of the Universe. The oldest globular clusters 
are generally given ages exceeding 16xl0 9 yrs although 13 x i0 9 
yrs probably cannot be excluded. A number of recent Hubble con- 
stant estimates give H = (10 * 10*yrs) ' * within ±10%, about twice 
the previous generally accepted values (which had a similar 
quoted error [3]. But H is the model age, since the big bang, 
of an unaccelerated expanding homogeneous isotropic universe. 
If there are stars within the universe older than H' 1 either 
one must abandon that model for the Universe or the Universe's 
expansion rate has been speeding up so that p+3p < in Eq.(2). 
This could be accomplished if p+3p were dominated by uniform 

2 

matter with -p=3p c > as suggested by particle theories, but 
with a hugely reduced magnitude for p . 

It appears that the only fairly secure regions of super- 
dense matter in our present universe are black holes where the 
properties and consequences are hidden from us and neut ron stars 
where the details of such matter can have some observable con- 
sequences. These will be surveyed in Section VI. 



46 



III. SUPERDENSE MATTER IN THE PAST UNIVERSE 

We live in an expanding reasonably isotropic and homoge- 
neous Universe at a temperature T^-3°K. We can safely extrapo- 
late back to an era (z ~ 3 * 10° ) where p^-10' 2 gem' and T^IO °K 
when the cosmic black body radiation last interacted with mat- 
ter. Extrapolations before that to vastly higher density and 
temperature regimes are all model dependent. But it is not im- 
possible that most of the en tropy per baryon was created in the 
Universe at this rather la te epoch although most models presume 
a very hot rather than cool big bang. The quasi -universal He 
abundance agrees with that from an isentropic extrapolation of 
a homogeneous universe back to kT ^ 1 MeV (T~i0 1O °/O and p ~40* 

_ 3 - 2 - 3 

g cm' of which /O(nucleon) ~ 10 gem 

If the Universe was exactly homogeneous and isotropic a 
past singularity in which matter had a density of order 
m (ir/m c)~ ~i0 gem' would be implied (as long as p+3p>0) 
[4] . Without such an extreme ideali zation we have only the Haw- 
king-Penrose theorems which prove that within every (past) light 
core of the Universe at decoupling there should be at least one 
past singularity [5]. But there is, at present, no proof that 
all or even most geodesies have an origin in such singularities 
or even, apparently, that the singularities are those associat- 
ed with an infinite density. There is no proof that before the 
present expansion phase the universe was not in a (inhomoge- 
neous) contracting phase and made the transition with some sin- 
gularities forming but most of the matter passing neither 
through states of Planck-like densities and temperatures 

(kT =m c ~10 GeV) nor even those where Grand Unified Theories 
P P 

are hypothesized to be relevant in establishing the net baryon 
excess [6]. If most matter were to survive from a contraction 
phase one might understand more easily how parts of the uni- 
verse, which in a homogeneous isotropic model could have had 
no causal connection at and since the big bang, nevertheless, 
appear so similar, as they come into view from opposite direc- 



47 



tions over our present hori zon. There could have been sufficient 
opportunity for homogeni za tion in the pre-expan si.on contracting 
phase. But in that case we might expect that we could not ex- 
plain the key cosmological numbers of our universe such as pho- 
tons per baryon by considering only the expansion phase since 
the last big bang. 

It is at present certainly more exciting to put aside the 
caveat that extrapolations back to near singular densi ties and/or 
temperatures may be mi sleading for mostofthe universe and fol- 
low the consequences of essentially homogeneous initially sin- 
gular models as they expand to the present. 

Elementary particle theories suggest two possib le types of 
scenarios, both of which incorporate extensions of the ideas of 
spontaneous symmetry breaking and gauge theories which seem to 
work so well in unifying the weak and electromagnetic inter- 
actions . 

In one set of models the universe is initially a cold set 
of quarks etc., and one identifies epochs and mechanisms for 
the generation of an entropy of 10 photons per nucleon as the 
matter expands. These will occur in the early universe if, for 
example, nucleation centers of expected first order phase changes 
are sufficiently rare that transitions (such as that from homo- 
geneous quark matter to separated tri -quark nucleons) are de- 
layed [7] . A second and. certainly more popular set assumes an 
initially hot expanding universe and attempts to account for 
the net baryon excess needed to give the present 10~ nucleons 
per photon. We shall consider below some examples of both sorts 
of models in which collective phase transitions unique to super- 
dense matter play crucial roles,' especially those associated 
with new symmetry breaking ground states which do not-have the 
full invariance properties of the Hamiltonian. 



48 



IV. COSMOLOGICAL PHASE TRANSITIONS OF SUPERDENSE MATTER 

The expected transition from quarks matter to nucleon mat- 
ter in an expanding universe raises two interesting questions. 
Could most of the entropy of our present universe have been 
generated in such a phase change of cold quasars? If quarks are 
not completely confined how many free quarks might be left over 
from the quark ~* nucleon transition regime in an initially hot 
big bang? [8] 

Lasher has made an initial exploration of the first ques- 
tion assuming complete confinement with quark-quark binding pnf 
ergy from gluons in a dilute quark sea proportional to the se- 
paration between the quarks and wi th parameters adjusted to fit 
the MIT quark model ofnucleons [7]. A tri-quark clustering into 
separate nucleons would have a lower free energy than a homoge- 
neous quark distribution at a density of order 10 gem . But 
if the transition is first order, the dilute quark phase can be 
" superextended" well beyond the transition point until reached 
by the growth of supercritical bubbles containing the nucleon 
phase, which were nucleated by random located fluctuations .This 
nucleation spacing is not calculated but adjusted so that the 
entropy generated from the delayed now irreversible transition 

9 

is the observed 10 photons per nucleon. This model universe is 

— A. 3 

about 10' s. old when the transitions begin but 2 x 10 s. old 
when all bubbles coalesce and there is no quark matter left. At 
that late time the baryon density has fallen to 10 gem . The 
amount of clumped matter in each bubble at coalescence is 10 Mq, 
about the mass of a globular cluster. He synthesis might take 
place in the 3 x 10 °K detonation wave associated with the ex- 
panding interface between the two phases. 

The energy U between separated quarks is presumed to grow 
linearly with separation for large r: 

U~(r/10~ 13 cm) GeV (3) 



49 



This approximation gives a reasonable fit to the Regge 
pole spectra of hadrons and to the excited states.of charmonium. 
Wagoner and Steigman have recently reconsidered the problem of 
the expected number of quarks (q) and antiquaries (q) left in 
our universe after the big bang cooling and expansion, if the 
difficult infrared problems of Yang-Mills gauge theories re- 
sults in a screening of the strong quark-quark force at very 
large distances L8J . By assuming that U of the form (3) remains 

— 1 3 2 

valid out to r = r c ~10 (2Mc /GeV) cm but stays constant at 

larger r, they construct a model for almost confined quarks of 
asymptotic mass M. Quarks can become truly free only when r> r , 
around the quark-nucleon transition region. For M ~ 15-30 GeV '/c 
this occurs in the relatively low temperature range kT» ~0. 2- 

-20 

Q.k GeV and gives a (q+q) to nucleon ratio of 10 , very much 
less than the ratio from earlier estimates which ignore the very 
large force range r . Because the frozen free quark to nucleon 

2 

ratio is proportional to exp(-Mc /kT*) even a doubling of the 

— 3 

assumed quark mass can make that ratio fall below 10' .A free 

2 

quark mass of order 10 GeV/ c would probably be needed to give 

- 20 

the 10 ratio in niobium implied by the experimental results 

of La Rue, Fai rbank , et al. [9] . It remains to be seen whether 
these results will be confirmed or contradicted by other ex- 
periments as well how free quarks and antiquarks might be ex- 
pected to attach to different nuclei during the compli ca te d sub- 
sequent history of matter during the condensations of the last 
5-10 billions of years. 

The most interesting and exciting conjectured phase tran- 
sitions in superdense matter are those associated with the sca- 
lar field condensates hypothesized to cause spontaneous sym- 
metry breaking in gauge theories of the elementary particles 
[10,2] ^ The prototype is the Weinberg-Salem theory: the initial 
symmetry with 4 massless vector fields is broken when the sca- 
lar Higgs-field with which they interact assumes a non-zero ex- 
pectation value in the ground state of the universe. This re- 
sults in 3 of the 4 vector fields acquiring a mass so that only 



50 



the electromagnetic quanta remain massless.But at sufficiently 
high temperatures there is a phase change in which the expec- 
tation value of the scalar Higgs-field condensate disappears 
and the state of lowest free energy in the universe is restored 
to the one of maximum symmetry . The high temperature phase tran- 
sition back to the maximally symmetric state could be blocked 
if there exists a sufficiently large excess of neutrinos over 
antineutrinos or vice-versa. The needed number density excess 
at the transition temperature T is typically of order (kT / c) , 

Q 

comparable to the density of thermal photons and 10 times 
greater than the net baryon excess. (Such an excess would great- 
ly affect the neutron -proton ratio in the temperature range 
10 -10 K and the amount of primordial He that would be for- 
med). Thus in a cold big bang the broken symmetry and scalar 
Higgs-field condensate could have existed in the early universe 
from the "beginning" with entropy created late enough so that 
the temperature T is never even reached. In the more conventional 

c 
hot big bang (without any huge v(v) excess) a phase change with 

resulting symmetry breaking i s expected as the temperature drops 

below T with kT ~ the rest energy of the scalar Higgs meson 

2 .2 

m.flC . Only if m„c £9 GeV can the transition be accomplished 
without passing through states of very much higher energy which 
would essentially freeze the "vacuum" into its initial symme- 

2 

trie state. For m„c £6 GeV the symmetric state without con- 
densate remains stable even at T=0. The proposed phase transi- 

- 9 

tion temperature kT >9 GeV would be reached about 10' s after 
the beginning of a homogeneous hot big bang when each species 
present had a density in excess of 10 g cm 

Since our present Universe has no large cosmological con- 
stant, the lack of scalar Higgs-field matter before the symmetry 
breaking transition must have contributed one. This would be 
equivalent to having "cosmological matter" present before the 

- 1 2 2 2 2 

transition with a density Pb ~40 m„m /c and pressure po=-PoC ., 

2 + 

with m. w the 10 GeV W mass acquired by the charged vector 



51 - 



fields after symmetry breaking. This densi ty is much larger than 
that of any single species at the transition temperature and 
may be larger than the sum of all one hundred of them. Then just 
before the transition the matter in our universe, "ordinary" 
plus "cosmologi cal" could have had a total pc +3p <0 [ll]. Be- 
cause the "ordinary" matter density and pressure continue to 
increase at still earlier times with, smaller particle separa- 

- 4 

tions as r , while po and po are independent of r, the total 
pc +3p cannot remain negative for times very much earlier than 
that of the transition. Although in principle Eq. (2) permits 
a closed universe to "bounce" without a singularity during the 

2 

interval in which pc +3p<0, such an early universe cannot be 
matched to our presently observed one in which the kinetic en- 
ergy of expansion is certainly not much less than the gravita- 
tional potential even at an age of 10 yrs. There is not enough 
time in the brief interval during which rofEq.(2) is positive 
to achieve the needed early velocity of expansion. 

If the symmetry breaking transition is a first order one 
with inefficient nucl'eation at T&T the interval of positive 

c r 

r might be greatly extended and the transition, when finally 
completed, would contribute a huge amount of additional entropy. 
In a contracting phase a similar delay would make the transi- 
tion even less able to cause a "bounce" before r becomes nega- 
tive again . 

In the conjectured Grand Unification Theories of strong, 
weak, and electromagnetic interactions the symmetri es are broken 
by another scalar field condensate. But the expected mass scale 
would have to be of order 10 GeV or greater if the proton is 

3 O 

to be stable against decay into leptons for at least 10 yrs. 
Such transitions would be relevant to the history of the Uni- 

— 37 

verse if one accepts an extrapolation back to a time 10 sec 

after a hot big bang begins in which the uni verse passed through. 

15 8 0—3 

a temperature kT ~ 10 GeV and density p^lO gem . Just how 
the transition was accomplished may, as in the Weinberg -Salem 
model, have an important effect on thermal history and entropy 



- 52 



generation in that era. But possible observable consequences 
in our present universe from such a phase transition at that 
time are difficult to predict as much for unknown particle phy- 
sics as for incomplete cosmological descriptions.lt is in that 
era that our present net baryon excess may have been fixed. .And 
for a particularly attractive class of models the transition 
should have been accompanied by a large production of magnetic 
monopoles. It is to this possible facet of phase transitions 
in superdense matter that we turn to next. 



V. MAGNETIC MONOPOLES FROM SUPERDENSE PHASE TRANSITION 

The strongly interacting elementary particles and the in- 
teractions they have among themselves are invariant under the 
non-abelian group of transformations SU(.3). Electromagnetic 
gauge invariance in which charged particle wave functions have 
the phases of their wave functions shifted in a well defined 
way when the vector potential undergoes a gauge transformation 
has the abelian group theoretic structure U(l). Thus the mani- 
fest symmetry of our present world is SU(3) X U(l). Before the 
phase transformation which broke the initial gauge symmetry of 
the Weinberg-Salam theory the unified weak and electromagnetic 
interactions had the group symmetry SU(2) x U(l) and the non - 
unified strong-weak -electromagnetic symmetries were those of 
SU(3)x SU(2) *U(1) . Grand Unified Theories assume that before 
the symmetry was spontaneously broken in some phase transform- 
ation, strong, electromagneti c, and weak interactions, mediated 
by massless vector bosons, were quasiequi valent and unified in 
some larger gauge group [12J. An attractive prototype for such 
models begins with an initial SU(5) gauge group. But when the 
symmetry of an initial non -Abelian group is spontaneously broken 
and the unbroken symmetry group contains the Abelian U(l) in 
its decomposition, the world with the broken symmetry can con- 
tain topologi cally stable magnetic monopoles L13].The monopole 



- 53 - 

mass M m is of order Uq where Mq is the characteristic mass ac- 
quired by previously massless vector bosons when the first spon- 
taneous symmetry breaking occurs leaving a U(l) factor [l 4] . 
Further symmetry breaking can extend the s tructure of the mono- 
pole but will not significantly change its mass. 

If the phase transformation occurs rapidly and quasi -uni- 
formly at T^T C , as should be the case, for example, if it were 
a second order transition , then <it appears difficult to account 
for the lack of observed monopoles if the general GUT symmetry 
breaking scenarios are essenti ally cor rect , and if, unlike quarks, 
magnetic monopoles are not "confined". Pairs of poles would be 

made by thermal fluctuations (near the transition the pole mass 

22/2 
^M m (l-T /T ) ) within expanding bubbles of nucleated matter in 

which the Higgs condensate had formed. In addition the Higgs 
field internal orientation in one bubble will initially be un - 
correlated with that of its neighbors until the independently 
nucleated bubbles coalesce. When they do the joining can result 
in topological "knots" which are stable monopoles and the anar 
logue of a surface sheet separating domains when a discrete sym- 
metry is broken as in the spontaneous magnetization below the 
Curie point of solid iron with a single alignment for easy mag- 
netization. According to -Guth and Tye the number of monopoles 
produced in this way does not differ hugely from the number of 
coalescing bubbles [15] . 

Zeldovich and Khlopov estimated the thermal production and 

■ 4. 
subsequent mutual ahnihi lation for poles of mass of order 10 GeV 

[16], They obtained an average remnant number density in our 
present universe of 10 cm , compared to the limits of 10 
10 cm from analyses of terrestrial and lunar surface matter 
and 10 cm in the interstellar medium from the longevity of" 
large scale Galactic magnetic fields. In a more refined analy- 
sis Preskill has considered the same problem for monopole mass 

M ~ 10 GeV [17]. Here the gravitational pull of the earth and 

-1 ° 
moon (10 eV/A) can be greater than the pole's binding to sur- 
face .matter so. that there may be surface depletion of poles. 



- 54 



6 2 1 

Interstellar magnetic fields of 3x10 G, uniform over 10 cm, 

11 -2 

would g i ve magnetic monopoles 10 GeV and v/c^lO ; a non - 

— 2 4- — 3 

relativistic pole abundance there of 10 cm is compatible 

with field survival. Such poles would still ionize like rela- 
tivistic nuclei with Z ~(X in incident cosmic rays. 

For such heavy poles to give an acceptable contribution 
to the present average mass density of the Universe, then aver- 

— 21—3 — 2 4- 

aged number density must be less than 10 cm , about 10 
less than the present number density of black body photons. In 
order to leave the conventional and successful He formation cal- 
culations in the 10 sec old universe unchanged, the pole/photon 

- 1 9 

ratio should not have exceeded 10 even then. Preskill, as 

Zeldovich and Khlopov, finds over 10 orders of magnitude too 
many magnetic monopoles surviving into the later universe if 
there was near thermodynamic equilibrium when they were made. 
Guth and Tye explore the possibility that a spontaneous sym- 
metry breaking phase transition which is first order may per- 
mit the needed huge suppression of pole creation. In this case 
large overextensions of the now metastable initial symmetric 
phase are possible if nucleation centers for the growing bub- 
bles of symmetry broken matter are sufficiently dilute. This 
would have two important consequences. First, the number of 
bubbles and thus the number of monopoles from mismatching Higgs 
condensates at coalescence can be greatly suppressed. Second, 
when most of the matter finally makes the symmetry breaking 
transition which allows the monopoles to form, the temperature 

2 

can be so far below kT and M c that thermal fluctuations pro- 
duce very few. According to Guth and Tye even after the latent 
heat release the initially supercooled matter temperature may 
not rise to near T . They suggest typical model numbers lead- 

, 10 _ ... 2 , _ ..14 



ingtoAf^ ~i0 GeV/c , kT c -10 GeV, supercool ing to kT ~ 10 GeV 
for most matter, and a release of latent heat which brings kT 

13' 

back to 10' GeV when the phase transi tion is finally accompli sh - 
ed. Such a model could suppress magnetic monopole production 



55 



sufficiently that calculated abundances are not embarrassed by 
confrontation with observational bounds .Whether .the phase tran- 
sition would actually go as suggested is, of course, less than 
clear. It is now almost 50 years since Dirac gave his strong 
aesthetic argument for monopoles. Perhaps we have been looking 
for much too light a particle in this half century and the ex- 

— 8 

pected history of a iO g magnetic monopole created in the early 
universe and strongly affected by gravitational and magnetic 
fields may be worth studying in more detail. 

VI. NEUTRON STARS [18] 

In comparison with the immense richness of ideas and phe- 
nomena associated with the conjectured behavior of superdense 
matter in the early universe, the physics of neutron stars may, 
for once, appear conservative and perhaps even pedestrian. But 
these are the only objects in our present universe where super - 
dense matter exists in a form where some relevant observations 
may depend on understanding such matter in quant itative detail. 
The unresolved questions are mainly technical. Even in the cores 
of heavy neutron stars the nucleon -nucleon separation is prob- 
ably not much less than half of what it is in normal nuclei. 
There does not appear to be a great likelihood that continued 
study and observation will tell us something really new about 
the nature of matter denser than that in nuclei which is also 
important in further understanding the nature of the elementary 
particles. 

However there are some questions about the nature of super- 
dense matter in neutron stars which can have observational 
consequences and which may be of some interest to particle phy- 
sicists and cosmologi sts. These concern 1) possib le quark cor es, 
2) 77-condensates and their properties, 3) neutron crystalliz 1 
ation, 4) the equations of state of cold neutron matter, 5) the 
equation of state of matter near the bounce of a dense stellar 



- 56 - 

core implosion. Some summary remarks about each of these will 
be given below. 

There is not yet a consensus on the equation of state of 

14 - 3 

cold neutron matter at densities > 2p (Po = 2. 8 x 10 gem 
= nuclear density) even if possible transitions to quark matter 
are ignored. This lack of agreement is a reflection of at least 
three unresolved quantitative problems. (1) What n-n potential 
should be used? The commonly applied Reid potential which gives 
a good description for nucleon scattering, when used with im- 
proved modern calculational techniques, seems to give too much 
binding and density for conventional nuclear matter. If this 
same potential is used for the almost pure neutron fluid cal- 
culations at higher densities , one would again expect that the 
resulting matter to be too "soft". (2) What nuclear force changes 
must be made because the n-n interactions take place in a super- 
dense ambient neutron sea? An important contribution to n-n 
attraction comes from double pion exchanges in which one of the 
intermediate states contains a ground state nucleon plus a 
A(T = 3/2, T=3/2) excited state nucleon (i. e. a tt -nucleon resonant 
state). In superdense neutron matter this attraction is dimin- 
ished by exclusion principle reduction of the available states 
for the intermediate nucleon , and by interactions of the inter- 
mediate baryons with the ambient neutrons. Thi s reduced attrac- 
tion gives an equation of state "stiffer" than that obtained by 
ignoring these effects of the ambient neutron sea but quanti- 
tatively accurate calculations are not yet available even for 
normal nuclear matter. (3) What are the quantitative effects of 
the "softening" expected from the condensation of pions into a 
coherent state in superdense neutron matter? 

The.A(7=3/2, T=3/2) pion-nucleon resonance caus es a strong 
p-wave attraction at energies below the resonance. This can be 
especially significant for 5? + n which is a pure T = 3/2 state. 
For a sufficiently dense n sea the total energy of some tt with 
momentum nk can become zero. At that critical density (p a ) the 



57 



neutron sea can begin' to lower its energy by converting some 
n to p+77 coherently, i.e. all the n~ form an essentially clas- 
sical state of wavenumber k with non-zero expectation value, 
while the neutrons near the top of the Fermi sea are a coherent 
mixture of neutrons with momenta p F and protons with momenta 
Pp-k. Exploitation of this possibility will clearly result in 
an equation of state "softer" than would be the case without 
it. (At p^3p >p a pion condensation has been estimated to re- 
duce neutron matter' pressure by a factor 4) [19] . The critical 
density for the onset of pion -condensation has been calculat- 
ed to be around 2p , but a definitive calculation would have 
to include neutron correlation and possible graphite like crys- 
tallization effects which depend upon an accurate application 
of known nucleon -nucleon forces in superdense neutron matter 
accurately calculating all three contributions to the equation 
of state simultaneously, i.e. the nuclear force including off 
energy shell contributions, changes in that potential from the 
dense ambient neutron sea, and pion -condensation is no easier 



3.0 

2M 

1.4 
1.0 

H 



. — MF 




J I I I L 



10" p,(gcm" 3 ) 



10" 



Fig. 1 

Masses of neutron stars M (divided by that of the sun, M§ ) versus central 
density p , Symbols are described in the text (after ref. 18). 



58 



than the still too difficult problem of solving any one of them 
definitively. 

The effects of the present uncertainties in the equation 
of state on neutron star structure is indicated in Fig.l where 
the masses of neutron stars is shown as a function of central 
density p [18]. The various curves correspond to different many 
body methods (MF=Mean Field) nuclear force approximations (R= 
Reid Potential, BJ = Bethe- Johnson) , effects of the ambient sea 
(TI = Tensor Interaction which includes stiffening from improved 
treatment of intermediate states with A), and 77-condensate ef- 
fects (tt,tt' with different but comparably reasonable parame- 
ters). The maximum possible neutron star mass occurs where 
BW/3p =0, and is different for the various models. The masses 
of neutron stars in binaries can, in principle, be determined 
when the companion is observable. Present estimates for six neu- 
tron stars are given in Table 1. All measured masses are con- 
sistent with M = l. [ t Mo, the horizontal line in Fig.l. None of 
the models is excluded. The radii and central densities for 
1.4 Mo neutron stars is given for the various models in Table 
2. The differences are very substantial as indicated by the 
particular example of Fig. 2 [20]. The Reid potential model has 
a large pion -condensate core; the TI model has such a low cen - 



TABLE 1 

Masses of neut ron . stars (N.S.) inferred from parameters 
of binaries (after ref .70) 



N.S. System 


U/Mo 


Binary Pulsar 


1.39 ± 0.15 


Her X-l 


1.30 ± 0.5 


Vela X-l 


1.7 ±0:3 


SMC X-l 


1.10 ± 0.6 


4U1538-52 


1.90 ± 1.1 


Cen X-3 


1.90 ± 1.2 



- 59 



TABLE 2 



Parameter of i. It A/ s neutron star models for a soft (R) 
and stiff (TI) equation of state 





R 


TI 


M/Mo 


1.4 


1.4 


R(km) 


10 


16 


4-4 2 
1(10 gem ) 


4.5 


11 


R(km) 


19 


4.7 









tral density at 1 . 4 M Q that its core has no pion -condensate at 
all. Although there may be some indications that the stiff er 
equations of state with larger radii give somewhat more com- 
fortable fits to some observations with accreting neutron stars 
in binaries, present data on radii and moments of inertia do 
not discriminate decisively among the models [20] . 

There are three effects unique to pion condensates which 
might signal the existence of such matter in the cores of neu- 
tron stars: (1) enhanced neutrino emission; (2) relaxation of 
magnetic fields; and (3) dynamic instability. 

1. The coherent meson field with finite wavenumber k has 
many of the properties of an external periodic potential in- 




VTI 



Fig. 2 

Sections of two neutron stars, one with a soft equation of 
state W) and one with a stiff one {TI) (after ref.20) 



- 60 - 

teracting with the degenerate core fermions. In particular it 
can effectively absorb a momentum k in the reactions n-^p+e+v 
and e+p -'n+y. Without some mechanism to absorb momentum (an- 
other neutron in modified URCA neu trino emi ssion ) neither reac- 
tion would be permitted in degenerate Fermi seas with the chem- 
ical potential balance E Jn) =EJp) +EJe) of a "low temperature" 
thermal equilibrium. But because of the enhancement of the pion- 
condensate such neutrino emission is the main mechanism for the 
initial cooling of hot neutron star cores . Fig. 3 shows estimates 
for the surface temperature of a neutron star as a function of 
time for two models, A , a 1.3 M Q , B=5 * 10 G, neutron star with 
a Reid potential soft equation of state and B, one with a stiff 
TI equation of state. The solid lines ignore pion- condensate 
neutrino cooling; the dotted ones include a maximum possible 
condensate cooling by assuming p=p ~3 x 10 gem' . Temperature 
bounds of possible neutron stars in four young supernova rem- 
nants (SNR) have been measured in a program which will even- 
tually observe 25 SNR of which 10 will be at a distance less 
than 10 light years. The ages and upper bounds to the surface 
temperature of a possible neutron star in the remnant are given 



a. 

E 

« 



o 



M = 13m0 






"■--""-■^Rl.. 


^\ 


— R 

— TI 


\ -A. 

v 


n-condens 
with psp 


i . i ... 


1 1 1 


1 J 



1 2 3 

log time(yrs) 



Fig 3 

Surface temperature versus age for model neutron stars 
described in the text (after ref.21) 



- 61 



TABLE 3 

Upper bounds to temperatures of possible neutron stars 
in young supernova remnants (&fR) (from ref. 22) 



SNR 



Tycho 

G 350.0-1.8 

W28 

G 22.7-0.2 



age (yr) 



400 
8 , 000 
3,400 

4 
10 



T *OX<*° *> 



2.0 -2.6 

2.0 -2.5 

1.75 -2.0 

2.2 - 2.7 



in Table 3 [22]. For the classes of models considered - and one 
might expect them to bracket a definitive one - some pion -con- 
densate may be necessary to explain the present observations 
unless none of these four SNR's contains an initially hot neu- 
tron star. But this would exacerbate the already puzzling prob- 
lem that there seem to be too many neutron stars formed (and 
observed as pulsars) even if all SNR's are associated with hot 
neutron stars. 

2. In neutron star core matter there is an equilibrium be- 
tween components in which those charged constituents which carry 
electric current can be converted into neutral ones which do 
not and vice versa. Thus e+p~~n+(v) in "normal" core matter and 
rr +p**n (or rr +n-~p) in pion condensate matter. In the first 
case Easson showed that no true equilibrium state is possible 
with j x B^O intheneutron core fluid [23] .However in that case 
a BCS energy gap so greatly suppresses the rate at which the 
§ x 3 x £~0 equilibrium is achieved, that this cause of disequi- 
librium can be ignored for well beyond the age of this universe. 
But for the pion -condensate where the BCS gap is suppressed and 
the conversion occurs through strong interactions even a very 

2 12" 

small j x B «Gp R (such as would be associated with B ^ 10 G 
where the ratio of LHS to RHS is 10' ) may result in signifi- 
cant and perhaps observable evolution of a pulsar's magnetic 



- 62 



field [24]. But no quantitative analysis of the relaxation rate 
has become available yet. 

3. If the transition between normal and pion condensate 
matter which begins at p=P a is a first order one, a neutron star 
whose central densi ty reaches p a may become dynamically unstable. 
According to Migdal the instability will occur if, at constant 
pressure, the density when the phase change is total exceeds 
3/2 p . The resulting implosion would be expected to release 
an energy comparable to the total gravitational binding energy 
of the star ~10 ergs. However, such implosions, even if pos- 
sible, should be extraordinarily rare. The critical core den- 
sity p could be achieved by accretion. But the maximum plaus- 
ible rate of mass growth, both theoretically and observational- 
ly, is 10 M®y and that is approached in fewer than 10 neu- 
tron stars in close binaries . Even if all such stars were within 
say 10' M® o f the critical mass which gives P=P a at the center, 
the rate of implosion in our Galaxy at present would be less 
than one each 10 years .Therma 1 cooling of a neutron star into 
the critical regime would be even less likely, except possibly 
within the first 10 seconds in the life of a newly formed hot 
(TZ10 llo K) neutron star. 

3 

In the density regime 1-10 p there may be two competing 
models for an adequate description of superdense matter. One 
begins with light quarks assumed to be in the asymptotically 
free regime; thi s is presumably appropriate at the highest den- 
sities. The other, appropriate for nuclear densities, consists 
of the much more detailed calculations on neutron, proton and 
pion constituents with a very small admixture of hyperon com- 
ponent in the baryon wave function . Since there is no large do- 
main in which both descriptions can be confidently and quan- 
titatively applied, there is not yet any reliable theory for 
the transition from nucleon (p ~p ) to quark (p » p ) matter. 
Therefore there is not yet any consensus on whether quark stars, 
i.e. stars whose cores are best described as almost free quarks, 



63 



can exist and even less on whether , i f they can exist, they would 
be formed in implosions. The mere existence question arises 
because there is a maximum mass for a neutron star, above which 
it will be squeezed into a black hole, regardless of the equa- 
tion of state of very superdense matter. Even for incompres- 
sible matter M<h/9 RG~ c . At the maximum model dependent mass 
the maximum central density is. also achieved. For the TI model 
this calculated p c ^10 gem' .Much softer equations of state, 
especially with pion condensates , may have maximum central den- 
sities a factor 10 higher. But most estimates for transitions 
to quark matter of soft nuclear matter suggest a transi tion be- 
ginning at 10 gem' with a jump to 10 gem' . However, the 
large uncertainties in nucleon equations of state together with 
those of quark matter leave it an open question whether quark 
cores could be achieved in neutron stars. 

Even if they are , quark cores would be expected only in a 
very small range of neutron stars with stiff equations of state 
despite a large "free" quark component andmasses and radii not 
strongly different from those achieved by some stellar models 
without quarks. In what qualitative way they would signal their 
presence is not clear since most neutron star in ternal phenomena 
(cooling, superfluid flows, etc. ) depend upon details at the 
top of the Fermi seas and these have not been explored for "di- 
lute" quark matter with any of the detail needed to discuss 
them for conventional "dense" neutron matter. 

There are in principle other transi tions of other entirely 
different kinds of matter which might also occur in the rela- 
tively small density regime Po <P < P nax such, for example, as 
those associated with transitions to new phases with Higgs type 
condensates. However there are no present indications of such 
transitions before P is reached. 

' n ax 

It is perhaps appropriate that the greatest progress in 
understanding superdense matter during the past year has prob- 
ably occurred in the finite temperature fixed entropy equation 
of state of such matter when the neutrinos from electron capture 



- 64 - 



by nuclei do not escape [25]. This seems to be appropriate for 
describing collapsing stellar cores which do not bounce until 
the equation of state of core matter becomes stiff (dp/dp > 4/3 p/p) ■ 
It now appears that the bounce and the shock wave it drives 
needed to convert the imploding star to a supernova, and leave 
behind a neutron star or black hole, will lie in the region 
p > pa - but probably not so far into it that classical nuclear 
matter calculations are not adequate. It is here perhaps that 
very classical "old-fashioned" nuclear physics is most likely 
to support a new important advance in understanding the astro- 
physical universe. 



REFERENCES 

[l] ZEL'DOVICH Ya. (1968) "Sov. Phys. Usp." 11. 38 

[2] LINDE A. (1979) "Rep. Prog Phys." 42, 390 and references therein 

[3] DE VAUCOULEURS and BOLLINGER G. (1979) "Ap.J." 233, 433 

AARONSON M. , MOULD J., HUCHRA W., SULLIVAN II W. , SCHOMMER R. and 
BOTHUN G. (1980) in preparation cfr. "Science" 207, 167 (1980) 

2 - 5 

[4] M is the "Planck mass" defined by GM =% c so that M ' ~ 10~ g. 

[5] HAWKING S. and ELLIS G. , "The Large Scale Structure of Space-Time", 

Cambridge University Press 1973 
[6] GLASHOW S. this conference 

[7] LASHER G. (1979) "PhysJ Revj Letters" 42, 1646 
[8] WAGONER R. and STEIGMAN G. (1979) "Phys. Rev. D" 20, 825 
[9] LA RUE G., FAIRBANK W. and HEBARD A. (1977) "Phys} Rev* Letters" 38 J_ 

1011 

LA RUE G, , FAIRBANK W. and PHILLIPS J. (1979) "Phys. Rev. Letters" 

42, 142; 42, 1019 
[10] KIRZHNITS D. (1972) "JETP Letters" 15, 529 

KIRZHNITS D. and LINDE, A. (1972) "Phys. Letters" 42B, 471 

WEINBERG S. (1974) "Phys. Rev." 90, 3357 



- 65 - 

[ll] KOLB E. and WOLFRAM S. (Nov. 197 9) Caltech preprint 

BLUDMEN S. (Nov. 1979) Univ. of Penn. preprint 
[12] GEORGI H. and GLASHOW S. (1974) "Phys . Rev. Letters" 32, 438 

GEORGI H., QUINN H. and WEINBERG S. (1974) "Phys . Rev. Utters" 33, 451 

GEORGI H. and NANOPOULOS D. (1979) "Phys. Utters" 82B, 392 
[13] t. HOOFT G. (1974) "Nucl. Phys." B79 , 276 

POLYZKOV A. (1974) "JETP Letters" 20, 194 

[l4] GOLDMANN T. and ROSS D. (1979) "Phys. Letters" 84B, 208 

[l5] GUTH A. and TYE S. -H. (Dec. 1979) SLAC preprint 

[16] ZEL'DOVICH Ya. and KHLOPOV « (1978) "Phys. Letters" 79B 

[17] PRESKILL J. (1979) "Phys. Rev. -Letters" 1,3, 1365 

[l8] BAYM.G. and PETHIK C. (1979) "Ann. Rev. Astron. Astrophys" Vol.17 

[19] AU C.-K. (1976) "Phys. Letters" 61B, 300 

[20] PINES D. (1980) "Science" 207 597 and references therein 

[21] TSURUTA S. (1979) "Phys. Reporta" 56, No. 5 

[22] HELFAND D. , CHANAN G. and NOVICK R. (1980) "Nature" in press 

[23] EASSON I. (1976) "Nature" 263, 486 

[243 RUDERMAN II. (1979) "Proceedings of CNRS International Colloquium on 
Physics of Dense Matter" in press 

MIGDAL A. (1979) Norditz preprint 

[25] LAMB D. , LATTIMER J.. PETHICI C. and RAVENHALL D. (1978) "Phys. Rev. 
Letters" kl , 1623 

BETHE H. , BROWN G. , APPLEGATE J. and LATTIMER J. (1979) "Nucl. Phys .A. " 



- 67 - 

SECOND SESSION 
21 st February 1980 - 3,30 p.m. 

Chairman: Nicolo Dallaporta 



GARY STEIGMAN 
ASTROPHYSICAL CONSTRAINTS ON NEUTRINO PHYSICS 

INTRODUCTION 

The early universe provides a stage on which the drama of 
particle physics is enacted. The high temperatures and densiti es 
reached during the early evolution of the hot big bang model 
afford the possibili ty of studying particle physics at very high 
energies. The "cosmic accelerator" will have produced particles 
too heavy and/or too weakly interacting to have been seen at 
terrestrial accelerators. These "relics" from an early epoch 
may influence the subsequent evolution of the universe and some 
may still be present today. By searching for such relics or, 
for their effects, information may be obtained which can be of 
value in helping define and constrain models of elemen tary par- 
ticle physics. The other side of the coin in this coherent ap- 
proach to particle physics and cosmology is that ideas and data 
from the world of microscopic physics may help in defining the 
parameters and models of the macroscopic world. The approach 
to particle physics via cosmology has been studied intensively 
in the area of neutrino physics. It is here that the subject 
is most mature in the sense that the constrain ts on the particle 
physics (masses, lifetimes, number of types) are truly cons- 



68 



training and, as well, there is significant feedback to the 
cosmology (constraints on the Hubble parameter, nucleon density, 
photon -to-baryon ratio). Here, then, I will concentrate on this 
specific example of the general approach to particle physics 
via cosmology. 

After a general discussion of the production and survival 
of particles during the early evolution of the universe (c.f. 
Steigman, 1979), I will specialize to the case of relic neu- 
trinos. It will emerge that stable ( t v ^ t % 1 - 2 x 10 yr.) neu- 
trinos must be lighter than a few tens of eV or, heavier than 
a few GeV . Neutrinos with intermediate masses must be unstable 
and their lifetimes may be constrained. In addition, there is 
from considerations of primordial nucleosynthesis, a limit to 
the number of "flavors" of light («lMeV) neu trinos . The under- 
lying physics which leads to the conclusion that there are no 
more than three or four, two - compon ent neutrinos will be out- 
lined. Analogous limits to other, more weakly interacting par- 
ticles will be mentioned. 

Equally important is the feedback from neutrino physics 
to cosmology. Improved limits may be set to the nucleon-to- 

1 

photon ratio (£ 4.2><10~ ) and to the present value of the 
Hubble parameter (H $.75 kms' 1 Mpc' 1 ; Hq 1 £ 13 * 10° yr) . In fol- 
lowing various arguments to their logical conclusions, we will 
close with the speculation (eagerly embraced by many at this 
meeting) that the "missing light" problem in clusters of ga- 
laxies has a natural solution if relic neutrinos have amass of 
the order of a few eV . 



THE COSMIC ACCELERATOR 

Much of the material pertinent to the discussion here has 
appeared in an extensive review by the author (Steigman, 1979; 
see also, Schramm and Wagoner, 1977). Here, then, I will out- 
line the relevant physics; for further details and references 



69 



to earlier work, the reader is referred to the aforementioned 
revi ews . 

To use the early evolution of the universe to study par- 
ticle physics, one assumption is crucial. The Cosmologi cal Prin - 
ciple (isotropy and homogeneity) is assumed to be valid for the 
epochs under consideration. The "standard" Robertson-Walker- 
Friedman (RWF) cosmological model is adopted, thereby simplify- 
ing the astrophysics used to probe the particle physics. Should 
any contradictions emerge from this approach, the fault may lie 
with the assumed particle physics, the adopted cosmological mo- 
del, either or, both. In any case, something new and important 
will have been learned. To date there is no compelling evidence 
which casts serious doubt on the assumption that the standard 
model provides an accurate description of the epochs of inter- 
est. For the most part we will be concerned here with times 

-s - 2 

~ 10 sec. when the temperature is £ 10 MeV, the particle num- 
ber density ; is £ 10' f" and the energy density is Z 1 keV f' 3 . 
Under such circumstances there is no reason to doubt the ade- 
quacy of the standard cosmological model or of conventional 
particle physics. 

Since the energy density in non -relativi stic particles 
(T < m) varies as p NR <cT and that in relativistic particles 
(flt=0 or m<T) as P^T , the early universe is "Radiation Do- 
minated " (RD). For RD epochs it is convenient to express the 
total density in terms of the photon density 



, m ,^ m; p ^, ^YiiyfiL). (1) 



-mm 



In (1), g(T) is the effective number of relativistic de- 
grees of freedom (spin states) at temperature T. 

g(T) =g B (V *^ g F (T). (2) 

In (2), gg(gf) is the number of relativistic boson (fer- 



70 



mion) spin states; the factor 7/8 arises from the difference 
between Fermi and Bose statistics ( c . f . Steigman, 1973). During 
the early, RD epochs, the age (or, its inverse, the expansion 
rate) and the total density are simply related (for details, 
c.f., Steigman, 1973, 1979). 

32tt 2 
Gpt =1. (3) 

Using (1) and (3), the age and temperature may be related 

t(sec)Tl eV = 2.i[g(T)]' Y2 . (4) 

To estimate the production and survival of particles in 
the early universe, it is convenient to compare the expansion 
rate (t ) with the collision rate, 

V(T) =n(T)<av> T xT 3 $(T). (5) 

An estimate of the number of collisions occurring when the 
temperature is ~T is 

r(T)t(T)<*T$(T). (6) 

Thus, at sufficiently high temperatures (provided 3 < * cr 
doesn't decrease too rapidly with increasing 7") the collision 
rate exceeds the expansion rate and the frequent collisions lead 
to the establishment and maintenance of equilibrium. 

As the universe expands and the temperatu re drops, the col- 
lision rate fails to keep up with the expansion rate (T « t ) 
and a critical temperature, T» , is reached below which equili- 
brium can no longer be maintained. Roughly speaking (for more 
details, see Steigman, 1979 and references therein), below T* 
no new particles are created and, none already present annihil- 
ate. Thus, for example, for particles of type i which decouple 
at I"*, the number in a comoving volume (a volume which expands 



- 71 



along with the average expansion of the universe), N-, is con- 
served: N i (T<T,) =N { *. For the most par t , the number of photons 

in a comoving volume is also conserved: n ccT 3 , V(T)a. T' 3 =tiV = 

r ' ' y 

=n y K = constant. There is, however, a very important exception 
to this rule. 

When the temperature drops below the rest mass of a par- 
ticle, the abundance of that .particle (relative to photons) 
decreases rapidly (« exp(-m/T) ) . The energy released by the 
disappearance of the non -rela ti visti c parti cles is shared by th e 
remaining .interacting particles. In parti cu lar, the photons are 
heated and, therefore, extra photons are created in every co- 
moving volume. The present ratio, then, of relic particles of 
type i to photons must reflect the extra photons produced after 
the relic particles decoupled at T* . 



(7) 



In (7) and elsewhere in this paper, the subscript o indi- 
cates the present value of the specific quantity. 

The importance of (7) is that, knowing the present photon 
number density, 



"ro sit00 \Yj) cm ~ 3 > (8) 




th a t r . £ t o ) 



the present density of relics i is known (provided, of course, 

to) 



(9a) 



Pio = m i" io • (9b) 




72 



With this general discussion as background, 1 et us now turn 
to the specific example of relic neutrinos. 



NUS FROM THE BIG BANG 

For neutral leptons, equilibrium is established and main- 
tained by the neutral current weak interactions 

e + +e~-*-*v i +P\ ; i=e,fi,r . (10) 

Note that for T « 100 MeV,the /J.' s and t' s have long since 
disappeared; still, the abundant e pairs ensure that v ' s and 
v t ' s are produced and kept in equilibrium. 

If we entertain the possibility that neutrinos need not 
be massless, it is convenient to separate the discussion of 
"light" neutrinos (m v «T„) from that of "heavy" neutrinos 
(T» ««„). 

Light Neutrinos 

For m v «T «M„, the cross section for reactions (10) va- 
ries as 

T 2 
<a v > 7 , = p(T)cc . (11) 

Equilibrium can be maintained (see (6)) down to T, ~ 1 MeV, 
at which time 

N *i\ 3 

(12) 



"r/. 8 Vl 



For massless neutrinos, g v . = 2; formassive neutrinos there 

i 
are two possibilities. 



73 



Majorana Masses: g v = 2, 

i 

Dirac Masses:* g = 4. 



(13a) 



In subsequent numerical estimates we will assume g = 2. 

i 
As the temperature drops below T* , the e* pairs annihilate 

when T$.m g , heating the photons relative to the neutrinos (c.f. 

Steigman, 1979), 



11 

4 



N ro 'TV • <1« 



The present density of li ght relic neutrinos is, therefore, 



<°vi = ■vi»vi~ i0 " 31 «vi«v i f-2^7) g cm " 3 - (15b) 

In (15b) and subsequently, the light neutrinos' mass is in 
eV. Light relic neutrinos then, with t %,to, will be about as 
abundant today as black body photons (although far more dif- 
ficult to detect) and may, if m v ~i eV, contribute significant- 
ly to the total mass density in the universe. 



Superweak Neutrinos 

There may be light neutral leptons whose weak in teractions 
are much weaker than the normal, full strength, neutral current 
weak interactions (e.g.: right-handed counterparts to the fam- 
iliar left handed neutrinos). Such neutrinos would have de- 
coupled much earlier in the evolution of the universe, at 
J 1 * >> 1 MeV (Steigman , Olive and Sc'h ramm , 1 97 9; hereinafter SOS). 
Such neutrinos do not benefit from any subsequent heating and 
their abundance relative to the ordinary neutrinos is diluted. 



- 74 - 



sir 
N v (T) = 



N 7 (T,) 



N y (T) 



NJT) 



(16) 



Similarly, their contribution to the total density is re- 



duced. 



SW 
g v (V 



N y (T*) 



,4/3 



NJT) 



g v (T). 



(17) 



Heavy Neutr inos 

The analysis of the survival of "heavy" neutrinos ( T* < m v ) 
is qualitatively similar to the previous discussion but, quan- 
titatively very different (Lee and Weinberg 1977; Dicus, Kolb 
and Teplitz 1977). At sufficiently high temperatures, even heavy 
neutral leptons will be relativistic and equilibrium will have 
been established early on. As the temperature drops below m v , 
the density of heavy neutrinos decreases rapidly (<Xi exp( -m v /T) ) 
and collisions become more and more infrequent, \gain, there is 
a critical temperature T*, below which few w pairs are created 
(since T^<m v ) and few existing vv pairs annihilate (since 
To! exp( -m v /T) ) . As before, the number of heavy neutrinos in a 
comoving volume is conserved and the present density of such 
relic neutrino s may be calculated ( Lee and Weinberg 1977; Dicus, 
Kolb and Tepliti 1977). 






6X10 



-8 



(18a) 



4.5 *10 



■28 



2.7. 



gem 



(18b) 



In (18) and subsequently, the mass of the heavy neut'rino 
is in GeV . Although the present number density of heavy relic 



75 - 



neutrinos is small, the contribution to the total mass density 
may be large. 

Before di s cuss in g the cosmo logical constraints on the mas- 
ses and lifetimes of light and heavy relic neutrinos, we turn 
to a consideration of primordial nucleosynthesis. We will out- 
line the underlying physics which leads to constraints on the 
number of types of light neutrinos and on the nucleon density. 
Armed with these constraints we will return to the question of 
the neutrino contribution to the mass in the universe. 



Primordial Nucleosynthesis 

Primordial nucleosynthesis provides one of the few probes 
of the physics of the early universe. In particular, the pri- 
mordial abundance of He leads directly to interesting cons- 
traints on the early expansion rate (Steigman ,Sch ramm and Gunn , 
1977; Yang et al. , 1979, hereinafter YS 2 R) and on the abundance 
of nucleons. The entire subject of primordial nucleosynthesis 
is the subject of an extensive review by Schramm and Wagoner 
(1977). Here, we will concentrate on those aspects of parti cula r 
relevance to the present discussion. 

For temperatures above ~1 MeV, the usual charged current 
weak interactions, 

p+e~*— n+v g , n+e + *-» p*-v g , n-p+e"+z7 , (19) 

maintain equilibrium between neutrons and protons. In equili- 
brium, the neutron-to-proton ratio would decrease as 

7' exp \~)- (20) 

At the same time that the weak interactions are turning 
neutrons into protons and vice-versa, deuterons are being pror 
duced by the strong interaction. 

n + p ■** D +7 (21 ) 



76 



But, the deuteron is only weakly bound and has a large 
photo -dissociation cross section. Since the density of photons 
capable of breaking up the deuteron is large, no sooner is a 
deuteron formed than it is destroyed. As a result, for T<-0.1 
MeV, the deuterium abundance is negligibly small and this pro- 
vides a bottleneck to the build up of heavier elements. All the 
while the neutron-to-proton ratio is decreasing. 

If equilibrium could be maintained by the charged current 
weak interactions (19), the neutron fraction would decrease ex- 
ponentially (20) and fewneutrons would be present when nucleo- 
synthesis could begin in earnest for T&0.1 MeV. However, for 
T^T^^l MeV, the weak interactions (19) "freeze-out" and the 
neutron-to-proton ratio decreases, but more slowly than would be 
indicated by (20). The number of neutrons (relative to protons) 
available for nucleosynthesis depends on T* through the compe- 
tition between the weak interaction rate, 

V WK (T) =n(T)$ WK (T) aT S , (22) 

and the expansion rate, 

t~ l (T) a lg(T)] 1/2 T 2 . (23) 

The neutron abundance at nucleosynthesis thus provides an 
estimate of the early expansion rate leading to tests of the 
standard model and to limits on g(T) (Steigman, Schramm and 
Gunn 1977 ; YS 2 R). 

When the temperature drops below ~ . 1 MeV , the deuterium 

3 3 

abundance increases leading to the rapid build-up of H, He 
and He. There is, however, no stable nucleus at mass-5. The 
difficulty of bridging this gap (recall that the density and 
the temperature are decreasing; the difficulty of overcoming 
coulomb barriers quenches rapidly any further reactions) pre- 
vents the synthesis of significant amounts of the heavier ele- 
men ts . Since He is the most tightly bound of the light nuclei, 



77 



virtually all the neutrons present when TZ0.1 MeV are incor- 

4- d. 

porated in He. As a result, the primordial abundance of He is 
most sensitive to the early expansion rate. There is much less 

... 4, 

sensitivity to the nucleon density but the He abundance does 
increase slowly with increasing nucl eon -to -photon ratio. The 
point here is that nucleosyn thesis begins ea rli er when the neu- 
tron abundance is higher. 

What is the primordial abundance of He? Observations of 
astrophysical obj ects (hot stars, HII regions, etc. ) wi th "normal" 
(i.e.: solar) chemical composition leads to helium abundances 
by mass, Y^O.3. But, clearly, at the same time that previous 
generations of stars were producing the heavy elements (remem- 
ber, no significant amounts of elements heavier than helium, 
with the possible exception of Li, could have been made in the 
big bang), they were also synthesizing He. Some fraction, 
therefore, of the presently observed He must have a stellar 
rather than a primordial origin. It is very difficult to de - 
termme precisely how much He is primordial. However, in re- 

... 2 

viewing the available data, YS R have set an upper limit of 
Yp^0.25 to the primordial abundance of He. The primordial 
abundance may be less than this but, there is no compelling 
evidence that Y p is much less (Ypk.0.23, Lequeux et al. ,1979). 

Constraints from Yp&O. 25 

The neutron-to-proton ratio "freezes out" when the weak 
interaction rate (22) and the expansion rate (23) become com- 
parable. The freeze-out temperature, T* , depends on the effec- 
tive number of spin states g* = g("T»). 

7\.ocg. . (24) 

The point is that, if more types of relativistic particles 
are present, the universe expands faster and the weak inter- 
actions drop out of equilibrium earlier, at a higher tempera- 



- 78 



ture. Thus, more neutrons are available and more He will be 
synthesized. For each "new" neutrino (i.e.: light, two-compo- 
nent neutrino with m v « 1 MeV and r v £ 1 sec, in addition to V g , 
V v r ), &Y*0.01 (YS 2 R). 

The helium abundance also increases with increasing nucleon 
abundance. Since nucleons are conserved (for T&10 MeV, baryon 
violating processes are entirely negligible), the nucleon-to- 
photon ratio at the time of nucleosynthesis can be related to 
the present nucleon -to-photon ratio: t\ = (n N /n y ) . An upper li- 
mit to Yp will, therefore, lead to upper limits to the number 
of types of neutral leptons, N L , and to the nucl eon -to-photon 
ratio T), 

Although the properties (mass, lifetime, spin states) of 
the r-neutrino are not terribly well established, it is reason- 
able to assume that there are at least three types of light, 
two- component neutrinos so that 2N L — 2g v ~ 6; N^ £. 3. In this 
case, for Y p &0. 25, the upper limit to the nucleon -to -photon 
ratio is 

77*4. 2xi0- 10 . (25) 

In the next section this limit will be used to constrain 
the mass in "ordinary" matter (nucleons) in the present uni- 
verse. 

Corresponding to a lower limit to rj (and, for Yp^O.25), 
there is an upper limit to N^ . Since we intend to entertain the 
possibility that ordinary matter need not dominate the mass in 
the present universe, i t is qui te difficult to obtain a reliable 
lower limit to tj. The reason is that most determinations of the 
mass do not distinguish between nucleons and, for example, mas- 
sive relic neutrinos (c.f. Gott et al.,1974). If, however, most 
of the mass is, indeed, in nucleons, then (Gott et al., 1974). 

7)^2.6*10'*°, (26.) 



id, for Y p £0.25, 



79 



N L £4. (27) 

In this case we obtain the fascinating prediction that, 
perhaps all the leptons to be discovered, have been discovered; 
at most there could be one new lepton type. 

In contrast, i f we live in a neutrino dominated universe, 
17 may be much smaller than the lower limit estimated in (26). 
In this case, for Y p 5.0.25, many more neutrino types would be 
permitted. Alternatively , for N L ~ 3 but 77 «10~ 10 , the predicted 
abundance of primordial He can be reduced considerably. Be- 
cause of the uncertainties in the particle physics and in the 
astrophysics, the unresolved issues here provide a striking 
example of the importance of a strong interaction between par- 
ticle physics and cosmology. 

Before leaving primordial nucleosynthesis, a comment re- 
garding constraints on super weakly in teracting particles (e.g. 
right handed neutrinos, gravitons, etc.). Such particles will, 
depending on their interaction strength, have decoupled before 
nucleosynthesis (ZlMeV). They will, however, if relativistic 
(m«l MeK), contribute to the total density at the time of 
nucleosynthesis. Their contribution will, however, be diluted; 
the earlier they decouple, the less they contribute (see (17)). 
More such superweak particles could exis t wi thout violating the 
nucleosynthesis constraints (SOS). For example (c.f. SOS), if 
there were right handed counterparts to the usual left-handed 
neutrinos which couple to a right handed intermediate vector 
boson which is sufficiently heavy, the v R ' s would have decoupled 
sufficiently early that their presence is consistent with 
Yp&0.25. The condition for this to be the case is (SOS) 

M w Z50M W ; T dec Z200 MeV. (28) 

One final remark. The ages inferred for globular cluster 
stars (Iben, 1974) depend on the helium abundance. The lower 
the helium abundance, the older the stars. For Y p 5,0.25, 



- 80 

t Z>13 x 10°yr (Iben, 1974). This lower limit to the age of the 
universe will be useful in constraining the possible values of 
the Hubble parameter. 



THE MASS OF ASTROPHYS ICAL SYSTEMS 

To place the question of neutrino masses in its proper 
context, an outline of the data relating to the mass on various 
scales in the universe is called for. For the standard R*F mo- 
dels without a cosmological term (A=0), there is a critical 
density separating those models which expand forever {p £p c ), 
from those which eventually stop expanding and collapse (p < Po) . 



p m IS°.Z 2xl0" 29 /.o (gem- 3 ). (29) 

c 8ttG 



In (29), G is Newton's gravitational constant and ffo is 
the present value of the Hubble parameter. To allow for. the large 
uncertainty in ffo (Sandage and Tammann, 1976; de Vaucouleurs 
and Bollinger, 1979; Branch, 1979; Aaronson et al. , 1979), H 
is written in terms of ho where, 

H =100 hofkais^Mpc' 1 ) ; H'q 1 = iO/io* x 10 9 yr . (30) 

The range in Hq is: O.U&ho&l. 

For each contribution to the mass density p- (where p =2^), 

introduce the dimensionless density parameter H f =p i /p 6 ; from 
(30) it follows that, 

p i =2><i0- 29 n.hl (gem' 3 ). (31) 

Of prime importance is the nucleon- to -photon ratio which 
may be expressed in terms of H^, ho and the photon temperature 
7V. 



- 81 - 



,.m* 3 *,<>-" f <y,*,(iiy. (32 , 

o 

Primordial nucleosynthesis provided an upper limit to 77 
for Tp £0. 25 and N L £3 (equation (25) ) which may be re-expressed 
as 

iy.o $0,014 (jy). (33) 

It is likely that 2. 7 &T &3 . 0°K , although, at present, 
there is some uncertainty regarding the preci se spectrum of the 
microwave radiation (Thaddeus, 1972; Hegyi et al., 1974; Woody 
et al., 1975; Danese and De Zotti, 1978). For T & 3.0 °K and 
/»o~0.4, there follows an extreme upper limit to the fraction 
of the critical density that could be in nucleons. 

n N $0.12. (34) 

This is an upper limit to the average density of ordinary 
matter in the universe today independent of whether the mass is 
in luminous objects such as main sequence stars or in non-lu- 
minous or under luminous objects such as large planets, dead 
pulsars, rocks, etc. 

The nucleon density is not measured directly. The total 
mass density is inferred from a variety of observations of as- 
trophysical systems of different scales .The most common approach 
is to utilize observations of velocities (redshifts) in a dy- 
namical analysis (Newton's laws.virial theo rem, etc . ) to derive 
the total mass of the system. A mass derived in this manner de- 



- 1 



pends on H Q : M<*R*-ho . Next, the light from the system is meas- 
ured and the luminosity is derived: L « R <*■ h ■ The mass-to- 
light ratio (expressed in so lar units Mq/Lq) is formed: Af/Loc/i . 
If, in. the universe, the mass and the light were similarly dis- 
tributed, the average mass density contributed by different 
systems (p i ) would be related to the average luminosity density 



- 82 



(*>) by the mass to light rat 



10 . 



" <t\ 



(35) 



However, as we will see, this does not seem to be the case 
and indiscriminate use of (35) may be misleading. Still, it is 
convenient (with the above caveat in mind) to compare the var- 
ious mass-to-light ratios to a critical mass -to -light ratio, 



(t) -£ 



(36) 



In a recent, extensive study, Kirshner, Oemler and Schecter 
(1979) have derived a value for the luminosity density which 
is consistent with that obtained by Felten (1977) from older 
data. 



d*2-*10 B h '(LJlpc- a ); (j\ 



~i. 4X4 




(37) 



In Table 1, mass -to -li ght ratios are presented for var- 



TABLE 1 
Mass of As trophys ical Systems 



System 


11/ L (Solar Units) 


Q (1) 


Solar Neighborhood (SN) 


2-4 


(0. 0014-0. 0029MO 1 


Galaxies (G) 


(8- 20) ho 


0.0057 -0.014 


Binary Galaxies and Small Groups (B) 


(60- 180) h 


0.043- 0.13 


Large Clusters of Galaxies (CI) 
Hot Gas in Clusters^ ' 


(280-840)h o 
(10-30) h' 1/2 


0.2-0.6 

-3/2 
(0. 0071-0. 021)h o 



(l)flis defined by M/L =Cl(M/L) . 

(2) From cluster x-ray emission, U Hr ~ 0. 1 (2ho) 



■3/2 



"TOT 



(Lea et al., 1973; Cavaliere and Fusco-Femiano, 1976; Malina et alp}, 1978). 



- 83 - 

ious astrophysical systems .based on data drawn mainly from the 
excellent review by Faber and Gallagher (1979).. For the reason 
cited above, the equivalent 0, presented to provide orientation, 
should be regarded with caution. Attention should, instead, be 
concentrated on an intercomparison of the various mass -to-light 
ratios. 

The "missing light" problem emerges clearly from the data 
assembled in Table 1: On larger scales, more of the mass is 
nonluminous. The inner, luminous par ts of galaxies are dominated 
by material which is somewhat less luminous ( per unit mass ) than 
the stars and gas in the solar neighborhood. This trend conti- 
nues and intensifies (less light per unit mass) onto the larger 
scales of binaries , small groups and large clusters of galaxies. 
The dual challenges are to determine what the nonluminous mass 
consists of and, why is there more of it on large scales. 

Some of the mass, clearly , is traceable to nucleons (e.g. , 
the stars and gas in the solar neighborhood). If, however, 
Q k,n ci Z 0.2 (Faber and Gallagher, 1979; Peebles, 1979), then 
ordinary matter (nucleons) would be incapable of accoun ting for 
for the bulk of the mass in the universe since primordial nu- 
cleosynthesis (equation (34)) limits the nucleon contribution 
to {Iff^O. 12. Thi3,then,is a clue that relic neutrinos may play 
an important role. 

If something other than nucleons contributes signi fi cantly 
to the total mass, it is difficult to separate out the nucleon 
contribution, The previous constraint would permit all of the 
mass (luminous and nonluminous), on scales up to binaries and 
small groups, to be due to ordinary matter. On the other hand, 
only for the solar neighborhood are the gas and stars observed 
directly. A firm but, perhaps, uninterestingly low, lower limit 
to f^ follows from (M/L) s/f : ^£i0~ ho . It should be noted 
that, if Qjj is this small, much less He and much more deuterium 
would have been produced primordial ly ; for N,=3: Yp&0.14, 
Xq<,10 . Alternatively, for such a small nucleon abundance, 
many more neutrino types are permitted by the nucleosynthesis 



- 84 - 

constraint. There is, however, good evidence, albeit indirect, 
for more mass in nucleons. 

If, as is likely, the inner luminous parts of ordinary 
galaxies are dominated by nucleons, Q.„ £,£!„. Support for this 
conjecture (£1^ &0 . 01) comes from the ^-ray emission observed 
from several rich clusters of galaxies. The %-rays are due to 
the thermal bremss trahlung emission of a hot intracluster gas 
(of nucleons!). Various estimates of the mass of the hot gas 
(Lea et al . , 1973; Cavaliere and Fusco -Femiano , 1976 ; Malina et 
al . , 1978), although uncertain, suggest that 

M T0T 
2SJ lc 7 

In summary, then, although 0,^ could, in principle be quite 
small (^y^iO" 3 ), a more likely range is . 01 £0^ £0 . 12. 

Estimates of the fraction of the critical density in var- 
ious forms (fi^) depend on the Hubble parameter and reflect the 
uncertainties . in Ho- Although the data only limit the range to 
0. 4 ~/»o ~i , it is possible to narrow this range. For the stand- 
ard RWF models (A=0),the expansion of the universe is deceler- 
ating so that the age (to) is always less than the "Hubble time" 
(flo 1 )- 

t &H0 1 ZlOho 1 xiO 9 yr. (39) 

For globular cluster stars, the age may be inferred (from 
theory plus observations) provided the helium abundance is 
known. For Y&O. 25, t *>13 * 10° yr (Iben, 1974) so that 

h £3/4. (40) 

There is, here, an interesting cosmic interconnection. If 
\Z0.01 (and N L ^3), then Y p <0.25 and the inferred ages of 
globular cluster stars will increase, restricting ho to even 
lower values. 



- 85 - 



THE MASS IN RELIC NEUTRINOS 

The contribution to the mass density due to heavy (» 1 MeV) 
or light (.« 1 MeV) relic neutrinos is (c.f. equations (15) and 
(18)), 

„ 2 fl.5 GeV\* ( T V 

„ eavy: n>0= (__j(_), (4i.) 

Light: H/io = •(— —J . (41b) 

8 v 200eV \2.7j 

The uncertainties in ho and To make an accurate estimate 
of 0- v (as a function of m v ) di fficu It. However, it is clear that 
relic neutrinos could dominate the mass in the universe (c.f., 
equations (33) and (41)). 

M TOT ^ n v ^ f 13Ge\'\ 
Heavy: — &— £ I 1, (42a) 

M LUM il N \ m v / 

M TOT ^ "v ^ rf gv \f m " \ 

Light: £— >2 (42b) 

"LOM ^ \2j\l.ieVj 

For i.4 eV&m v &13 GeV , the universe is neutrino dominated. 

Heavy, relic neutrinos will cluster in systems formed by 
non -di ssi pati ve gravitational collapse (Steigman et al.,1978). 
They would, therefore, be expected to contribute to the non - 
luminous mass in binaries, smal 1 groups and large clusters. The 
x-ray emission from clusters suggests a limit to non-nucleonic 
matter: Mj^j.^-20 M«; heavy neutrinos would contribute too much 
unless m v ~3 GeV. 

Light neutrinos, in contrast, find it more difficult to 
cluster (Tremaine and Gunn, 1979);the lighter the neutrino the 
less likely it is to cluster. Depending on their mass, light 
relic neutrinos may cluster in the deep potential wells of clus- 
ters of galaxi es whi le avoiding significant clus tering on smal ler 



86 



scales. Here, then, is a promising solution to one of the puz- 
zling aspects of the missing light problem. Relatively light 
(m v & 10-20 eV) relic neutrinos will contribute to the total 
mass of as trophy sical systems in exactly the manner required to 
explain why the nonluminous mass fraction increases on larger 
sea les . 

Very light neutrinos (m v ~i eV) won' t cluster at all; their 
contribution to the total mass in the universe could be signi- 
ficant (M v ^Mfi) but is unlikely to be dominant. 

Relatively heavy (m v ^20 eV) , light relic neutrinos would 
contribute too much nonluminous matter on small scales. For ex- 
ample, a Majorana neutrino (g v =2) with m £ 28 eV would force 
M TOT Z,20 M N . 

In summary, then, there are three categories of interest. 

(i) Relic neutrinos with m v £i eV or m v %.13 GeV could not 
supply the dominant contribution to the mass in the universe. 
Masses consistent with these limits are allowed astrophysi cal - 

ly- 

(ii) Relic neutrinos with 1 &m v &30 eV or 3 &m v &13 GeV 
could dominate the mass in the universe. Neutrino masses in 
these ranges may be further constrained by more detailed astro- 
physical considerations (galaxy formation , dyn ami cal evolution, 
stellar structure, etc.). 

(iii) Relic neutrinos with 30 eV &m v 5,3 GeV are, if stable 
(T~ v Z,t ), excluded, because they would contribute too much to 
the presently observed mass in the uni verse . Detai led consider- 
ations (Dicus et al., 1977; Gunn et al , , 1978) suggest that 
neutrinos with masses in this range must decay quickly. Unless 
t ^ ^10 sec, the decay of such relic neutrinos would either pro- 
duce too many gamma rays, distort the microwave radiation or 
adversely affect primordial nucleosynthesis. 



- 87 - 
SUMMARY 

The current interest in the approach to particle physics 
via astrophysics and cosmology is certain to intensify in the 
future. Neutrino physics provides a beacon illuminating the po- 
tential value of this cosmic connection. The feedback from the 
particle physics to the astrophysics will be of great value in 
expanding this approach. 

Light (m„ « 1 MeV) or heavy (m v » 1 MeV) neutrinos would 
have been produced copiously during the early evolution of the 
universe. If stable'or long-lived, relic neutrinos would have 
survived to influence the subsequent evolution of the universe. 

Light neutrinos, in particular, would help determine the 
expansion rate at the time of nucleosynthes is . If the primordial 
abundance of He is Y p &0.25 then, the presence of three, light 
neutrino types (v g , v , v r ) leads to an upper limit to the pre- 
sent nucleon-to-photon ratio: 77^,4.2 x 10' .This limit ensures 
that no more than 12% of the critical density could be in the 
form of nucleons: ftyy ~0. 12. Furthermore ,i f the helium abundance 
in old, globular cluster stars is Y&0.25 then the age of such 
stars exceeds 13 billion years. This constrains the uncertain 
Hubble parameter to H %,75 kms Mpc .Given that massive relic 
neutrinos may dominate the mass in the universe, the nucleon 
contribution is difficult to estimate . It is likely that Uy £ 0. 01 ; 
for 77>i><40 and Y p £.0. 25 there could be, at most, one new 

lepton type: N L £4. 

If neutrinos are not massless, heavy or light relic neu- 
trinos could dominate the mass in the universe. This would be 
the case, for r v > t Q , provided that 1 <m v £.30 eV or 3 <m v <13GeV. 
For masses in the range 30 eV £m v J$J GeV , the neutrinos would 
have to be short-lived (t v < 10 sec). Lighter (m v <l eV) or 
heavier (m v >13 GeV) neutrinos are consistent with cosmological 
constraints but such relic neutrinos would not dominate the mass 
in the universe. 

Finally, it was noted that light relic neutrinos may pro- 



- 88 



vide a solution to two aspects of the missing light problem. 
Since most of the mass in the universe is non -luminous, it is 
clear that massive relic neutrinos (heavy or light) could be 
viable candidates. Heavy neutrinos, however, would probably con- 
tribute too much dark mass on small scales. In contrast, light 
neutrinos with m v £,10 eV will find it difficult to cluster on 
all but the largest scales where the missing light problem is 
most striking. This property provides support for the specula- 
tion that neutrinos do indeed have a mass and that the heaviest 
neutrino weighs ~ 10 eV . If correct, the implications for par- 
ticle physics and for cosmology of this speculation would be 
profound. At the very least, there would be a new perspective 
to the puzzle of the existence of the neutrino. Why, of course, 
the neutrino exists to supply the mass of the Universe! 



ACKNOWLEDGMENTS 

I wish to thank Giorgio Salvini and the other organizers 
of what has been a stimulating meeting from which I learned a 
great deal. In the work summarized here, I have profitted great- 
ly from many colleagues. I particularly wish to acknowledge my 
frequent col labor.ator Dave Schramm and his colleagues at Chi- 
cago, Keith Olive, Mike Turner and Jongman Yang. In addition, 
I have learned much from conversations with John Ellis, R.Bar- 
bieri, and L. Maiani. This work was supported by DOE Grant ER- 
78-8-02-5007. 



89 



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AARONSON M., MOULD J., HUCHRA J., SULLIVAN W. T. , SCHOMMER R.A. and BOTHUN 
G.D. , "Ap. J." (In Press, 1980). 

BRANCH D. (1979), "MNRAS" 186, 609 

CAVALIERE A. and FUSCO- FEMIANO R. (1976), "Astron. and As trophys . " 49, 137 

DANESE L. and DE ZOTTI G. (1978), "Astron. and As trophys." 68, 157 

DICUS D. , KOLB E.N. and TEPLITZ V. (1977), "Phys. Rev. Lett." 39, 168 

FABER S.M. and GALLAGHER J.S. (1979), "Ann . Rev. As tron . Astrophys . " 17, 135 

FELTEN J.E. (1977), "Astron. J." 82, 861 

GOTT J.R. , GUNN J. E. ..SCHRAMM D.N. and TINSLEY B.M. (1974), "Ap. J. " , 19 4 , 543 

GUNN J.E., LEE B.W., LERCHE I., SCHRAMM D.N. and STEIGMAN G. (1978), "Ap. 
J." 223, 1015 

HEGYI D. , TRAUB W.A. and CARLETON N.P. (1974), "Ap. J." 190, 543 

KIRSHNER R.P., OEMLER A., Jr. and SCHECTER P.L. (1979), "Astron. J." 84 , 951 

LEA S.M., SILK J., KELLOGG E. and MURRAY S. (1973), "Ap. J. (Lett.)" 184, 
LI 05 

LEE B.W. and WEINBERG S. (1977), "Phys. Rev. Lett." 39, 165 

MALINA R. , LAMPTON M. and BOWYER S. (1976), "Ap. J." 209, 678 

PEEBLES P. J.E. (1979), "Astron. J."S4, 730 

SANDAGE A. and TAMMANN G. A. (1976), "Ap. J." 210, 7 

SCHRAMM D.N. and WAGONER R. V. (1977), "Ann. Rev. Nucl. Part. Sci." 27, 37 

STEIGMAN G. (1973), "Cargese lect. Phys." 6, 505 

STEIGMAN G. , SCHRAMM D.N. and GUNN J.E. (1977), "Phys. Lett." B66, 202 

STEIGMAN G. , SARAZIN C.L. , QUINTANA H. and FAULKNER J. (1978), "Astron. J." 
83, 1050 

STEIGMAN G. (1979), "Ann. Rev. Nucl. Part. Sci." 29, 313 

STEIGMAN G. , OLIVE K. A. and SCHRAMM D.N. (1979), "Phys .Rev. Let t. " 43, 239 

THADDEUS P. (1972), "Ann. Rev Astron. Astrophys." 10, 305 

TREMAINE S. and GUNN J.E. (1979), "Phys. Rev. Lett." 42, 407 

deVAUCOULEURS G. and BOLLINGER G. (1979), "Ap. J." 233, 433 

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YANG J.,. SCHRAMM D.N., STEIGMAN G. and ROOD R.T. (1979), "Ap. J." 227, 697 



91 



ETTORE FIORINI ( * > 
NEUTRINO EXPERIMENTS IN THE LABORATORY . OPEN PROBLEMS 

1 . INTRODUCTION 

I would like to discuss here a few subjects of neutrino 
physics which are in my opinion of consi derable interest in the 
study of common problems of physics and astrophysics. After a 
short description of the various artificial sources of neu trinos 
at different energies and of the corresponding detectors, I will 
review the most recent experimental 1 imi ts on neutrino mass and 
half-life. The problem of the conservation of lepton numbers 
will then be considered in some detail, also in view of the pre- 
sent limits on neutrino oscillations. 

A brief review of some problems in charged and neu tral cur- 
rent neutrino physics in the laboratory will conclude thi s talk . 



2. SOURCES OF LOW AND HIGH ENERGY NEUTRINOS 

The most natural source of low energy neutrinos is, of 
course, radioactivity, but all experiments at low energy have 
however been carried out with power nuclear reactors, where low 
energy antineutrin os are copiously produced by fission of 3S (J 

239 

and Pu. If one takes into account that about 5.34 antineu- 

trinos are emitted per fission, that about 200 MeV of energy 
re produced and that about a thi rd of this energy only is used 
as electric power, one obtains that the rate of antineutrino s 
produced per second by a nuclear plant is: 



a 



(*) Istituto di Fisica dell ' Uniyersit^ di Milano. Is tituto Nazionale di Fi- 
sica Nucleare - Sezione di Milano. 



- 92 - 

20 , 

(1) R m 5 x 10 X P antineutrinos/ second 

where P is the electric power. The neutrino flux in a detector 
placed, say, at ten metres from the centre of the reactor core 
i s: 

(2) $=Jxi0 13 v e ' s cm'* s~ X 

for a reactor of one Gigawatt electric power. 

Most of the experiments carried out so far have been per- 
formed at the Savannah river plant , which , being a mil itary reac- 
tor, has been constructed underground, unlike the plants pre- 
sently being built for production of commercial power. Che has 
to note in this connection that an underground source of neu- 
trinos is in general preferable , since the cosmic ray background 
is considerably reduced. 

Preliminary measurements have been carried out LlJ at the 
Caorso reactor, located on the Po river near Piacenza in Italy 
(Fig.l), where the detector can be placed at 10.5 m from the 
centre of the core. The only reactor specially built for neu- 
tron and neutrino physics is located in Grenoble and has a power 

12 — 

of 57 Megawatt only, with a flux on the detector of $ = 10 v g ' s 
cm" s" . Access and facilities are however far superior in this 
reactor than in those constructed for military reasons or for 
nuclear power production. The antineutrino energy spectrum ex- 
tends from zero to about 6 MeV, with a maximum at about 2 MeV. 
Detectors are usually made of plastic or liquid scintilla- 
tors, sometimes doped with Gadolinium to detect neutrons. In 
hydrogen one can have a rate of a few events per kgr per hour, 
if the detection efficiency is near tc* one. In complex nuclei 
this rate can be considerably lower, since Pauli principle re- 
duces strongly the cross section per nucleon. In the detectors 
presently being planned the rate can however be on thousands 
events per day, thus allowing a real ' "on line" monitoring of 
the performance of the reactor. 



93 




Fig. 1 
The power reactor of Caors (Piacenza) 



94 - 



Neutrinos of intermediate energy can be produced at the 
so called "pion factories" where beams of intermediate energy 
(from 500 to 800 MeV) protons are available at intensities of 
hundreds of microamperes. There are three of these pion fac- 
tories presently available: LAMPF in Los Alamos, Triumf in Ca- 
nada and SIN near Zurich in Switzerland, but only at Lampf are 
neutrino experiments actually being performed. 

These experiments are of the "beam dump" type: namely the 
protons are stopped in a massive target. Since negative pions 
are absorbed, neutrons and antineu trinos are produced by pion 
and muon decays according to the sequence: 



(3) 



77 -*/i. + + V 



u 






which is the only one allowed by the additive law. 

The spectra of these neutrinos and an tineutri nos are shown 

7 t -2-1 

in Fig. 2. Intensities of about 10 neutrinos cm s are ex- 



e 

a. 

CO 



cc 

IU 



1 


f' /^~i 


^ 


/ 


7\ 




// 


/ \ 
\ 




// 


\ 
\ 




// 




^y 


\ 





10 20 30 40 50 

NEUTRINO ENERGY (MoV) 



Fig. 2 
Neutrino spectra from a proton beam dump 



95 - 




a. 



PC 
w 
o 



be 

-H 



|S 



o 
o 



96 - 



pected on a detector placed at about 10 m from the centre of the 
dump. Since the cross sections are only three orders of magni- 
tude more than those for reactor neutrinos, while intensities 
are millions times less, the rate of neutrino interactions is 
quite lower. Since however their energy is larger, the back- 
ground is also much lower, also because of the low duty factor 
of these machines. 

Detectors for neutrino interactions at pion factories are 
quite massive and are made of scinti llators, Cerenkov detectors 
and spark chambers. 

High energy neutrino (antineutrino) beams are produced by 
the decay of positive (negative) pions and kaons generated by 
proton interactions at the high energy accelerators (Fig. 3). 

Intense pion and kaon beams can be focused acromati cal ly 
by means of magnetic horns or qua drupoles, they are left to de- 
cay in a vacuum or- air pipe. Muons and hadrons in the beam are 
stopped by a very massive shield (Fig. 4), and only the neutrino 
component is left [2]. Energy spectra of these "wide band" neu- 
trino beams are shown in Fig. 5. When positive pions and kaons 
are focused the neutrino beam is mainly made of muon neutrinos, 
with "impurities" of muon ant in eu trinos, electron neutrinos and 

-2-2 - 3 

antineutrinos of the order of 10 ,10 and 10 , respectively. 
For negative pions and kaons the impurities in the muon anti- 
neutrino beam can be evaluated accordingly. 

Dicromatic neutrino (antineutrino) beams can be produced 
by fosusing positive (negative) pions and kaons of a fixed mo- 
mentum P. The neutrino energy spectrum then present two peaks: 
one due to pion decay and corresponding to ~0.45P, and the 
other corresponding to kaon decay, with a momentum of ~0.95P 
(Fig. 6). 

Detectors at these energies can be either bubble chambers 
(Fig. 7), or counter calorimeters (Fig. 8 and 9). Since cross sec- 

— 3 B — 3 6 2 

tions ranges from 10' to 10 cm for neutrino energies from 

1 to 100 GeV, and the flux can be as high as 10 v' s cm" per 



97 - 



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98 - 



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99 - 



pulse, one expects an event rate ranging from 0.005 to 0.5 
events ton pulse" . The masses of counter calorimeters can 



50 



100 



150 



300 








50<R<75cm CC Events 






__l 






J\ 




200 




















2^ 


L_ I 


— 


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100 








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200 



Etot(GeV) 



Fig. 6 
Energy spectra of a dicroraatic neutrino beam 



be of many hundreds of tons, and statistics totalling millions 
of neutrino interactions are at present possible. 

It is interesting to compare the properties of the neu- 
trinos produced "artificially", with those of neutrinos from 
natural sources which are mainly of three types: 

a) neutrinos from the sun. As pointed out in other talks 
at this conference these neutrinos have fluxes on the surface 
of the earth of the order oilO v '& cm' s '., and energies of 
a few MeV , comparable to those of the reactor antineutrinos . 

b) neutrinos from, gravitational collapse . If ~ 10 neu- 
trinos are emitted in a gravitational collapse occurring at a 

2 2 

distance of about ~ 10 cm from the surface of the earth, their 



x on a terrestrial, detector ranges from 10 to 10 v ' 

-2-1 e 



flu 
cm "s 



Their energies are of a few tens of MeV, similar to 



- 100 - 




c 



IZS 



£ F^^l 



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J2 



3 

er 



ui 01 



J5 



101 



those of neutrinos produced in beam dumps of the protons in a 
pion factory. 



-Sm_ 




Fig. 8 
The experimental set-up of the CDHS collaboration 



c) atmospheric neutr inos . These neutrinos are produced by 
the decay of pions, kaons and muons generated by interactions 
in the earth's atmosphere of cosmic rays hadrons. Thei r flux is 

- 2 - 1 - 1 

less than one cm sr s and mainly (two thirds) in the hori - 
zonthal direction. The energy spectrum of these "natural" neu- 
trinos L 3 J is very similar, as shown in Fig. 10, to the spec- 
trum of neutrinos produced by protons of 10 GeV interacting on 
a "bare" target, namely without any focusing of the secondary 
pions and kaons. One has to note 'however that the compositions 
of accelerator and atmospheric neutrinos are different: in the 
former case the beam is pratically made only of muon neutrinos, 



102 - 



while in the latter electron neutrinos account for a third of 
the total flux. This is obviously due to atmospheric muons, which 
are allowed to decay on very long lengths in the upper atmos- 
phere. 



LAST 12 PLANES 

OF THE 

TARGET CALORIMETER 



PROPORTIONAL 
TUBES 

MARBLE 



SCINTILLATORS 




TOROIDAL 
RON MAGNETS 



IRON FRAME 



Fig. 9 
The experimental set-up of the CHARM collaboration 



Interactions and properties of atmospheric neutrinos can 
be well investigated in labora tori es situated deep underground, 
where the muon and neutron background is strongly reduced , whi le 
the neutrino flux is pratically unaffected. 'This will be a very 
interesting "subproduct" of most underground experiments to 
search for nucleon decays, The rate of neutrino events in the 
designed detectors can be of hundreds per year [4]. 



- 103 



10 



if O.I 



O.OI 



O.OOI 




Argonne 
focused 



Atmospheric 



_I_ 



4 
GeV 



Fig. 10 

Comparison of various "artificial" neutrino fluxes 
with the energy spectrum of atmospheric neutrinos 



3. NEUTRINO MASS AND STABILITY 



The best limit on the mass of electron antineutrino can be 
obtained from the fit to the predictions of the V-A theory of 
the energy spectrum of the electron in the decay: 



(4) 



3„ 3„ _ _ 

■Ji -* 2 He + e + v 



The precision of this measurement is due to the very low 



- 104 



transition energy for this decay (18.6 keV) .Recently Tretjakoff 
et al. [5], have obtained from this decay: 

(5) m - <35 eV at 90% confidence level. 

e 

This limit, which is already at the same levei of atomic 
and molecular energy, seems hard to be improved. 

A limit on the mass of the electron neutrino can be ob- 
tained from the positron energy spectrum in the decay: 

22 22 



(6) uNa -• ioiVe + e + + v, 

where however the transition energy is much larger (545.7 keV) 
and consequencially the result (6) poorer: 

(7) m v <410O eV at 67% c.l.. 

e 

I will not discuss here the limits of the electron neutrino 
masses deduced from cosmology, which will be considered else- 
where in this conference. 

The limit on the mass of the muon antineutrino has been 
obtained from the study of the decay: 

(8) tt + - ^ + +v^ 



an 



d is C7): 



(9) m v <510 keV at the 90% c.l.. 

The present limit on the mass difference between muon neu • 
trino and antineutrino, on the other side, is L8J : 

(10) m -m- < 450 keV at the 90% c.l.. 

fj. fi 

A massive neutrino could decay: 

(ID V (e.») -y +X 

where X i s an unidentified nuclear object. 



- 105 



The corresponding limit can only be given in the neutrino 
centre of mass system and depends therefore on, the neutrino 
mass. 

From a reactor experiment Reines et al. 19 J obtain for the 
electron antineutrino : 

(12) r v < 300 sec. m v (in eV) 

e e 

while for the mu on neutrinos the Gargamelle Collaboration gives 
[10]: 

(13) r <1.2 x 10~ 2 s m v (eV) 

(14) r_ < 3 x 10' 3 s m- (eV) 

fj. M 



4. CONSERVATION OF THE LEPTON NUMBERS 

According to the additive law we can group together the 
leptons (e~ ,v ,n~ ,v ) and the antileptons (e ,V e ,/i ,v ) (ne- 
glecting for the sake of simplicity the r leptons and antilep- 
tons) . 

The conservation of the lepton number can be studied by 
means of double beta decay of nucleus (A,Z) into nucleus (A,Z+2), 
when single beta decay to the intermediate nucleus (A,Z+1) is 
either energetically forbidden or at least strongly hindered 
by a large change of the (parity -angular momentum) state. The 
decay can in principle occur in two channels: 

(15) (A,Z) - (A,Z+2) +2e~ +2v g 

(16) (A,Z) - (A,Z+2) +2e~ 

where the latter,' which would imply lepton non conservation; 
would be strongly enhanced with respect to the former one due 
to phase space. In addition, the distribution of the sum of the 



106 



two electron energies would show a peak corresponding to the 
transition energy. 

Double beta decay can be studied with geological methods: 
a rock containing nucleus (A,Z) is examined chemically and with 
mass spectroscopy to find abnormal isotopic aboundance of nu- 
clei (A,Z+2). Positive results have been obtained for Se , 

12 8 13 

Te and Te , and the half lives so obtained are not in dis- 

agreement with theoretical predictions for two neutrino double 
beta decay. One has to note however that the effect could have 
been produced by processes other than double beta decay in such 
a long geological time. Direct distinction between two -neutrino 
and neutrinoless decays is moreover impossible [ill. 

Direct experiments based on the detection and measurement 
of the two emitted electrons have been attempted by many authors, 
but only lower limits on the half life for neutrinoless double 
beta decay have been obtained. In order to reach a positive re- 
sult, at least for the two-neutrino mode, the Milano group is 
at present investigating in a low background laboratory in the 
Mont Blanc tunnel double beta decay of e0 Nd into an excited 
level of 62 Sm by searching for the de-excitation gamma ray. 

It is obviously possible that mu on and electron numbers 
are separately violated, while the total lepton number is con- 
served. The following limits on this possibility have been ob- 
tained at 90% confidence level: 

K L -/i + +e + 

(16) < 2xi0" 9 [12] 

K i -'all 

± _ ± + - 

(17) — ■< 1.9 xjQ' 9 [13] 

/a* -all 

Many experiments have been carried out to search the 
decay : 

(18) (i + - e + +y 



- 107 



by measuring in coincidence the photon and positron energies. 
Limits on the branching ratio of 3. 6 x 10~ 9 , .1.1 x 10'° and 
1.9*10' have been obtained at Triumf [14], SIN [15] and 
Lampf [16], respectively. In this last laboratory the goal is 

• • - 1 2 

to attain a sensibility of 10 

The direct transition of a muon into an electron in the 
field of a nucleus has been recently searched at SIN [17], and 
the following limit has been obtained: 

32_, _ 32 _ 

(19) — < 0.7*10 

\x + o -> capture 

In the same experiment a limit has been set on the pos- 
sibility that, according the suggestion by Konopinsky and Mah - 
moud, leptons are grouped as follows: 

(2°) (V e ~'V +J and ( U e' e *' V f ,^~) 

which would allow convertion of a negative muon into a positron. 
This effect has not been found, with a limit: 



32„ + S2„. 

(21) " + S ~ e + Sl <9*1Q- 10 



— 3 2 

f-i * S — capture 

This limit is however model dependent. 

An experiment has been performed recently at Lampf on the 
validity" of the multiplicative law, according to which only the 
expressions : 

(22) 2 (VV and ('*) * 

are separately conserved. If the additive law is valid only the 
sequence (3) is possible in a beam dump, and therefore only muon 
neutrinos and an tineu trinos and electron neutrinos are emitted. 
According to the multiplicative law also the sequence 



(23) 



- 108 



w*-*/i + + v u 



L 



e + y + v 

e m 



is possible, and electron antineutrinos are also emitted. The 
experimental set-up, shown in Fig. 11, consists of a Cerenkov 
tank, which can be filled with heavy or light water, shielded 
with lead, scintillators and drift chambers [18] . 



SCINTILLATOR 
ANTI-COUNTERS 




DRIFT CHAMBER 
ANTI- COUNTERS 



CERENKOV 
DETECTOR 
(6 tons H2O 
or D2O) 



Fig. 11 
The experimental set-up by Burman et al. 



When filled with D 2 the detector is sensitive to the 
normal charged current reaction: 



(24) 



v + d — p + e + p 



for which about 20 events per day are expected. The process is 
indeed found, with a cross section of: 



(25) 



cr= (5.6 ± 1.6) x 10' A1 cm 2 /v 



- 109 



which compares well with the predi ction of the V-A theory , tes ted 
for the first time at this energy: 

,„.. „ observed 

(26) R = = 1.17 ±0.32 

predicted 

When filled with water the detector indicates no evidence 
for the reaction 

(27) v g +p - n +g* 

which would indicate validity of the multiplicative law. The 
limit at 90% confidence level is: 

(28) R = < 0.05 

fJ- -'all 

Limits on neutrino mass and on lepton conservations are 
strictly connected to the problem of neutrino osci 1 lations, which 
will be taken up later on by L.Maiani. According to the hypothesis 
first put forward by Bruno Pontecorvo an originally "pure" beam 
of muon (electron) neutrinos of momentum P, would contain, af- 
ter a distance R, an impurity of electron (muon) neut rinos.The 
ratio would be 

V*'^ / R 

(29) \ =0.5 sin 2 2a(l-cos 2tt — 
I v (R.P) \ L 

where the oscillation length L is given by 



(30) L = — , with M'^\mj. -ml\ 

M 

Up to now the best limit on v j^s v g oscillations at the ac- 
celerators has been obtained by the Gargamelle collaboration [19] 
and is reported, as a function of the mixing angle a, in Fig. 12. 



- 110 - 



A corresponding limit on v g ~^ v oscillations, obtained 
at nuclear reactor by Reines et al. [20], yields M<0.4 eV . 



> 
3 

5 





^-0045 
/^-0.064 


LIMITS ON NEUTRINO OSCILLATIONS 

a) 68%c.L 

b) 95 %c. 1 




a 




^^^r-^-^--^ 




aP^-— 1 === === — _. 



sin 2a 



LIMITS ON ANTINEUTRINO OSCILLATIONS 

a) 88 % c. I. 

b) 95 % c. I 




sin 2a 



Fig. 12 

Limits on neutrino and antineutrino oscillations 
by the Gargamelle collaboration 



- Ill 



New experiments at nuclear reactors by the Irvine group and by 
Grenoble group should reach a sensitivity of 0. 01 ,eV for maximum 
mixing angle. 

Good limits on neutrino oscillations with sensitivities 
from 0.01 to 0.001 eV, could be an interesting subproduct of 
the underground experiments on nucleon stability. One could in 
fact search for anomalies of the ratio between electron and muon 
neutrinos as a function of the zenithal angle. 



5. CHARGED CURRENT NEUTRINO INTERACTIONS 

I will be concerned here only with the cross sections of 
charged current neutrino interactions at the various energies. 
At low energy these cross sections can be calculated rather pre- 
cisely by the V-A theory for the "inverse beta decay" process: 

(31) v+p— e + +n 

e r 

which can be studied at nuclear reactors. Unfortunaly only one 
rather old experimental result, obtained by Nezrick and Reines 
[21J, exists, and yields: 

(32) cr gxp = (0.94 t0.13) xiO~* 3 cm 2 

in good agreement with theoretical predictions .There is no doubt 
that this experiment should be repeated soon. 

In a recent experiment on weak neutral currents at the same 
reactor [22], which we are going to mention later, the Irvine 
group have obtained for the process: 

(33) v +d-*e + +n+n 

e 

a cross section: 

(34) <r = (1.5 ±0.4; xjo" 45 cm 2 



112 - 



in good agreement with theoretical predictions: 

obs e rved 



(35) 



R 



predicted 



= 0.7 ±0.2 




eJGeV) 




Fig. 13 

Cross section for charged current neutrino and 
antineutrino interactions at the CERN PS 



- 113 - 



.3 

X 



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o 



U(9V)U 



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- 114 



Cross sections for interaction of reactor ant in eu trin os 
on complex nuclei have also been obtained; thei r interpretation 
in the frame of V-A theory is however more complicated due to 
the difficult evaluation of nuclear matrix elements. 

At intermediate energy we have already reported the result , 
obtained at LAMPF, on the cross section for the disintegration 
of deuterium by neutrinos (reaction (24)). 

At higher energies the situation is totally di f f eren t sin ce 
nuclear effects disappears and theory predicts that cross sec- 
tion should increase linearly with energy, as expected for neu- 
trino interactions on a point-like object. This is already found 
at energies of a few GeV, as in the experiments by Gargamelle 
at the CERN proton sincrotron (Fig. 13) [23]., and well confirmed 
at higher energies, as shown in a recent review [24] (Fig. 14) . 



6 . NEUTRAL CURRENT NEUTRINO INTERACTIONS 

As shown in Fig . 15, 1 eptoni c weak interactions by electron 
neutrinos and antineutrino are a mixture of neutral current 
and charged current (diagonal) interactions. On the contrary 
scattering on electron by muon neutrinos and antineutrinos can 
occur only via neutral current. One has tonote in addition that 
cross sections for neutrino interactions L2] are proportional 
to the mass of the target: leptonic neutrino interactions are 
therefore expected to occur with a rate lower by three orders 
of magnitude with respect to the semileptonic one. A clear se- 
paration of these rare events from backgroundis therefore quite 
di f ficu It . 

Only one experiment has been carried out at low energy L25J 
with antineutrinos from a nuclear reactor on electrons. Since 
both neutral and charged cur rent are present the cross sections 
obtained experimentally are compared with the prediction of the 
V-A theory for charged current only. The cross sections are: 

(36) a exp = C° 87 l°- 5 ) a V-A and Cr exp= ( L7 ±0 -4) a V-A 



115 - 



— £, 



--o- 



V. 



- J? 



+ 



-_^_ 



K 



-o— .- 



Fig. 15 

Elastic scattering ofelectron and muon 
neutrinos on electrons 

for antineutrinos in the energy ranges 1.5-3 MeV and 3-4.5 MeV, 
respectively. This corresponds to an electroweak angle of: 



(37) 



sin & sw = 0.29 ± 0.05 



Experiments at particle accelerators on scattering in elec- 
trons by muon neutrinos and antineutrinos have been reviewed 
recently by K. Winter [26]. The results agree with values for 
the electroweak angle of:: 



s in 6: 



(38) 
respectively . 



'sw 



+0.08 o +0 09 

0.22 and sin 6 ew =0.23 



-0.05 



^5 If 



-0.23 



- 116 - 



Liquid 
scintillator ~ 
anticoincidence 



Ten 3 He 
proportional- 
Counters 



Lead 



D ? 0- 



Cadmium- 

Sheet 

(O.I cm) 



It Meters 
Reactor 



Center v~ 




' — j |— I0.8cm \-SOc 



m 



Fig. 16 

The experimental set-up used by the Irvine group at the Savannah 
River reactor to study neutrino electron elastic scattering 

An important result on semi 1 eptoni c neutral currents has 
been obtained recently by the Irvine group, in an experiment 
[22] (Fig. 16) on the reaction 



(39) 



v + d — v + p + n 

e e r 



- 117 



It is interesting to note that the cross section for this 
reaction, due to low energy , depends only on the .axial term and 
is therefore independent on the electroweak angle. The ratio 
between the expected and predicted rates for reaction (39) is 
found to be 

' exp 38 i 9 events day 

(40) R — = - *0.8±0.2 

pred 50 ±3 

with an experimental cross section of 

(41) <r exp -(3. 8 -t0. 9) 10'** c*/v e 

From the experiments described so far, those on semilep- 
tonic interactions at high energy reviewed in [26], and the re- 
cent results on parity violation in the scattering of electrons 
on hydrogen and deuterium, obtained at SLAC, one has 

(42) sin 2 $ sw = 0.230 10.009 

7. CONCLUSIONS 

I would like to conclude this brief review with the fol- 
lowing conclusions: 

a) intense sources of "artificial" neutrinos are at pre- 
sent available from nuclear reactors, pion factories and high 
energy accelerators. It is therefore possible to reproduce ac- 
curately enough the properties of "natural" neutrinos reaching 
the surface of the earth. 

b) all present results are in agreement with massless and 
stable neutrinos. Theoretical limits obtained in astrophysics 
are however still much lower than those obtained in "terresr 
strial" experiments. 

c) no evidence has been obtained so far for neutrino oscil- 



- 118 



lations, but limits are going to be much improved soon in ex- 
periments with neutron reactors and low energy proton acceler- 
ators. Atmospheric neutrinos can represent a powerful tool for 
the study of these interactions, expecially in the massive ex- 
periments presently being planned underground to search for nu- 
cleoli decay. 

d) charged current cross sections increase linearly with 
the neutrino energies up to the maximum values available at pre- 
sent (~ lOOGeV). 

e) properties of weak neutral currents are at present reas- 
onably well established: they violate parity and conserve 
strangeness and charm. 



REFERENCES 

[l] FIORINI E. : Low energy weak interac tion "Proceedings of the Inter- 
national Conference 'Neutrino 79', Bergen (Norway) 18-22 June, 1979" 

L2J FIORINI E.: Weak interactions at low and high energies - to be pub- 
lished 

[3J CERN, Frascati, Milano, Torino Collaboration: Proposal to carry out a 
background calibration for a proton-lifetime detector- CERN/PSCC/80-70 

[4] Frascati -Mi lano-Torino Collaboration: Proposal for an experiment on 
nucleon stability with a fine grain detector - Preprint 

L5j TRETYAKOFF E.T. et al . : "Proceedings of the International Conference 
on High Energy Physics, Tbilisi, July 1976" Volume B, 118 

[6] BECK E. and DANIEL H. (1968): "Z. fur Phys." 216, 229 

[7] DAUM T. et al . : "Phys. Lett." to be published 

[8] BRICMAN C. et al . (1-978) : Re vi ew of particle properties "Phys. Lett." 
75B, 1 

[9] REINES F. et al . (1974): "Phys .Rev. Lett . " 32, 180 

[10] BLIETSCHAU J. et al. (1978): "Nuclear Phys." B133, 205 

[ll] FIORINI E.: Double beta decay - Invited Paper to the "int.Conf.on Neu- 
trino Physics and Astrophysics; Baksam Valley, June 1977 



- 119 



[l2] KORENCHENKO S.M. et al. , BARASH- SCHMIDT N. et al., (1978), Review of 
particle Properties "Phys. Lett." 75B, 1 

[l3] KORENCHENKO S.M. e t al . (1976): "Soviet Phys.JEPT" (,3, 1 

[14] DEPOMMIER P. et al . (1977): "Phys. Lett." 39, 1113 

[l5] POVEL H.P. et al. (1977): "Phys. Lett." 72B , 183 

[16] BOWMANN J.D. et al. (1979): "Phys .Re v. Lett. " 42, 556 and private com- 
munication 

[17] BADERTSCHER A. et al. (1979): S SIN Newsletter" 12, 13 

L18J BURMAN R.L.: Presented to the International Conference on "Neutrino 
Physics and Astrophysics - Bergen, June 18-22, 1979" 

[19] BLIETSCHAU J. et al . (1978): "Nuclear Phys." B133, 205 

[20] SOBEL H.W. et al. (1976): "Proc. of the 1976 International Conference 
on Neutrino Physics and Astrophysics - Aachen pag.678 

[21] NEZRIK F.A. and REINES F. (1966): "Phys. Rev." i 42 , 852 

[22] PASIERB E. et al . : Presented by H.W. Sobel to the 1'979 International 
Conference on Neutrino Physics and Astrophysics, Bergen, June 18-22, 
1979 

L23J Aachen, Bruxe lies, CERN, Ecole Poly technique, Milano, Orsay, U.C. London 
Coll: Nuclear Phys. B85, 269 (1975) 

[24] STEINBERGER J. (1979): Selected Topics in Neutrino Interactions "Lec- 
tures Given at the University of Haway Summer Institute" 

[25] REINES F. et al. (1976): "Phys. Rev. Lett." 37, 315 

L26J WINTER K. : Review Talk given to the Chicago Conference on Lepton and 
Photon Interactions at High Energy, August 1979 - Preprint. 



- 121 - 

LUCIANO MAIANI (,) 
NEUTRINO OSCILLATIONS 



Abstract 

Neutrino oscillations are reviewed, both for'Dirac and Majorana neu- 
trinos^ Consideration of neutrino masses in unified arid grand-unified gauge 
theories leads to expect non-vanishing, non-diagonal neutrino masses, in a 
range suitable for neutrino oscillations to be seen. Finally , a recent anal- 
ysis of the CERN beam dump experiment suggesting V — ► u oscillations is 
illustrated. 



INTRODUCTION 

Neutrino oscillations arise if neutrinos havealepton num- 
ber or lepton flavour violating mass. Very small masses are 
needed for neutrino oscillations to be observable in the range 
of energies available at present. Masses from the order of 10 2 eV 
downwards give rise to oscillation lengths larger than 1 m at 
an energy of about 1 GeV. Osci llations of the electron neutrino 
into the muon, or r, neutrino, for masses above 10' 6 eV and 
sizeable non-diagonal terms, could explain the low level of so- 
lar neutrino events observed, as compared with the expected 
rate. 

The possibility of neutrino oscillations and their impli- 
cations in the case of the solar neutrino experiment have been 
known for a long time [l , 2 ] . The reasons for looking again at 
this problem can be summarized as follows: 

i) The present view of particle in teractions , based on the 
principle of gauge invariance, makes it unlikely that quantum 



(*) .Istituto di Fisida dell' Universita' - Roma. 



122 



numbers like the lepton (or baryon) number are exactly conserv- 
ed.not being coupled to massless vector bosons. 

ii) Concrete examples of grand unified theories show that 
a non-diagonal mass matrix for neutrinos has indeed to be ex- 
pected, with neutrino masses in the range appropriate to give 
rise to detectable neutrino oscillations. 

iii) The results of the beam dump experiment recently per- 
formed at CERN may be interpreted, al though very speculatively, 
as positive evidence for v ■*-»-v T oscillations. 

In this talk I shall mainly concentrate on po int (ii) above, 
namely neutrino masses in unified and grand unified theories. 
This will be preceded by a short reminder of the general fea- 
tures of neutrino oscillations, both in the Di rac and in the 
Majorana case. 

Finally, the bearing of the CERN beam dump experiment on 
neutrino oscillations will be illustrated, in comparison with 
data from other sources. 

OSCILLATIONS OF DIRAC NEUTRINOS 

Let the weak charged lepton current be of the form 

j k = ^y\( i -y^) v e *Pv\(i-VB)v lt ^y\(^-y^ v r + • • • = 
= 2 £ T w y x (vjL 

w-e , H, . . 

(L = left-handed) and let us introduce lepton flavour non-con- 
servation by giving neutrinos a non-diagonal Dirac mass 



2? n = T, i (Z w ) R M wu .(v v ,) l 



(2) 



As a consequence, the fields N i which correspond to the 
mass eigenstates (mass-neutrinos) are related to the fields in 



- 12 3 - 
(1) (current-neutrinos) by unitary transformations 

< v Jl = U .i( N i)L 



(3) 



The weak current in terms of mass -neutrinos takes the mixed 



foi 



^ = 2 £ l w T\V wi (N i ) l 



(4) 



W, I 



We can now discuss neutrino oscillations. Suppose that a 
decay takes place at the origin of coordinates, with emis- 
sion of, say, an e . The neutrino emitted in the decay is thus 
a V eL' tne li ne ar combination of mass -neutrino fields deter- 
mined by Eq. (3). After a length L.and if the masses of JV • are 
different, the various components of v , acqu ire different phase 
factors, so that the state is now a superposition of v . v 
etc. If energy is sufficient, it may produce leptons of dif- 
ferent flavours. In formulae, the probability for a v to os- 
cillate, for example into a v „ at a length L, is given by 
(E»m.): 



P(v e -V 



E £/ exp [i(m\-m 2 )L/2E]U* ' 



(5) 



For N flavours, the matrix U is described by (N-l) 2 real 
parameters, and we have N-l mass-squared differences. Hence the 
oscillation probabilities depend upon a total of N(N-l) real 
parameters. Even if U has large non-diagonal elements, to see 
the effect of oscillation L must be sufficiently large, so that 
at least some phase factor has had time to become of order unity. 
From Eq. (5), and for a given neutrino energy E, we see that 
this requires- 



I Z *ij(Ej =t,TTE/\m\-m)\ 



(6) 



124 



for some i and j. In turn, if we deal with an experiment with 
a given source-to -detector distance L and with a typical neu- 
trino energy E , this experiment is sensitive to neutrino os- 
cillations for mass differences 



A m ^V2£~~7T (7) 



typ 

For Am near the bound (7), the energy spectrum of the 
charged lepton produced at the detector will be modulated in a 
way which would give conclusive evidence for v oscil lations ( as - 
sum in g point-like source and detector). If Am is much larger 
than the bound (7) , and the osci llation length much shorter than 
L for practically all energies in the spectrum, we can observe 
either a reduction of the diagonal probability, P(v e —v g ) < 1, 
or a non-vanishing off-diagonal probability, these effects be- 
ing constant over the energy spectrum. Figu re 1 illustrates the 
range of Am which can be explored in some characteristic ex- 
periments where neutrino osci llations have been, or can be, look- 
ed for (provided U has sufficiently large non-diagonal ele- 
ments ) . 

In the same figure: 

i) the cosmological upper bound to the sum of the masses 
of light stable neutrinos [3] : 

2 m i <h0 eV (8) 

ii) the experimental upper bound to the mass of the neu- 
trino emitted in the (3 decay of tritium [4] 

m v <35 eV (9) 

e 

are also indicated. 



125 



MAJORANA NEUTRINOS 

Neutrinos may well be Majorana parti cles, namely particles 
described by a spin 1/2 field <//, such that 

* - *C 

(C=charge conjugation). In the special represen tan tion for the 
Dirac J matrices we shall adopt (the Majorana representation), 
the above equation reads simply 

■A = + do) 

i.e. ■ V is a real field [5]. A massless, left-handed, neutrino 
can be easily arranged into a Majorana field. We set 

*' V L +( v Oc mv L +V L (ID 

The left-handed component of \p is just v L and its right- 
handed component is the antineu trino. 

Masses can be given to N Majorana fields by a coupling of 
the form 

^ = &5 TO , v., + </£( iy y B )P ww , </v (12) 

(sum over repeated indices understood, T means transposition, 
the Majorana representation is adopted and, consequently, 5 and 
P are real, symmetric matrices). Written in terms of the L and 
R components of \p, a Majorana mass term is seen to transform, 
for example, v L into (v L ) c . If we ascribe, as usual, lepton 
number L = + l and L = -l to v L and to (v L ) c , respect ively, a Majorana 
mass has thus AL = 2, besides it being able to violate lepton 
flavour . 

The mass term (12) can be diagonalized [6] by defining 
ass-neutrino fields according to 

N. = U* . (v t ) +U . (v\) (13) 

l II l I'll »l' I/» VJ-O; 



m 



126 - 



U is, in general, a complex, unitary matrix, but, nonetheless, 
N. is still a real spinor. Note that, if we express the weak 
current in terms of mass neutrinos we obtain again precisely 
the expression (4). Actually, because N i is real, we may write 
Eq. (4) in two equivalent ways: 

J K 'KVkV-ytWniBi -•"ho'Y X (l*V*)U 9i (l 9 ) c (14) 

Equation (14) shows explicitly that negative helicity neu- 
trinos are coupled predominantly to e , fi , etc , while they 
couple to e , jj. , etc., only with probability of order (m/E) . 
The opposite holds for positive helicity. For the mass range we 
are interested in, and for all the weak processes available (in- 
cluding double 3 decay): 

(m/E) 2 £(keV/MeV) 2 =10'° 

Thus, to all practical purposes, lepton number is con- 
served in weak processes, as opposed to lepton flavour. The os- 
cillations of Majorana neutrinos are the same as those of Dirac 
neutrinos, including the possibility of CP violating effects L7j 
in the case where U is a complex matrix. 



NEUTRINO MASSES IN THE STANDARD THEORY 

Quark and charged lepton masses are measured in MeV or 
GeV L8J. Why then should neutrino masses fall in the peculiar 
range shown in Fig.l, where oscillations can be seen? We shall 
examine this question first within the standard gauge theory of 
the electroweak interactions [9]. 

In the next section, we shall consider grand unified the- 
ories (GUTs) . The standard theory is based on the gauge group 

H =SU(3) col ®SU(2)<8>U(l) (15) 



- 127 - 



(GM^ 



II 



Mai , r 



aMGMo,)- 1 



(GMa)" 1 



KT 



KJ 4 



KP 



B £ -decay 



10° 



co smo log leal 
bound 



10 m(eV) 



cosmic rays *9 



reactor |- 



low energy ace. 



high energy ace. 



Fig. 1 

The range of neutrino masses explored in different Z-'-osci 1 la tion 
experiments .Details of the experiments can be found in the talks 
by E, Fiorini and by C. Rubbia at this Conference. The two upper 
bounds marked on the mass scale correspond to (i) the bound to 
the mass of the neutrino emitted in the (3 decay of tritium and 
(ii) the cosmological bound to the sum of light stable neutrino 
masses. In the upper part of the figure some estimates of light 
neutrino masses in grand unified theories are reported (see text, 
Section 5). 



Left-handed fermion fields are classified into weak iso- 
doublets 







128 - 



and right-handed fields are taken to be weak isosinglets. Be- 
sides vector and fermion fields, one has to introduce Higgs, 
scalar, fields; in the simplest version, one complex isodoublet 
suffices: 

*■(■!*) 

Sometimes it is useful to introduce explicitly the charge- 
conjugate o f 4>, namely 



(17) 



If we assume that the standard theory is the fundamental, 
final, theory of particle interactions, we must allow in the 
Lagrangian only renormali zable couplings. The restriction to 
renormali zable couplings leaves essentially two possibilities 
to give neutrinos a mass. 

i) v^ exists. If right-handed neutrinos exist, then we may 
have an H- in variant Yukawa coupling of the form 

where I ^ is one of the left-handed doublets. When 4> Q takes a 
non -vanishing vacuum expectation value, the coupling (18) gives 
rise to a neutrino Dirac mass, of the form (2) with 

M „„< - *../ «A>>o * g.„« (G f ) * (19) 

G p. being the Fermi coupling constant. The situation is entirely 
analogous to the quark and charged lepton case. Since we know 
that the quark mass ma trix is non -di agon al (at least the Cabibbo 
angle is non -vanishing) we expect M , to be so. However, for 
neutrino masses to be in the eV region, we need peculiarly small 
Yukawa couplings 

^neutrinos- W ' - 10 " 9 ) g c „ . , ep ,. (20) 




129 - 



ii) No v R . It is widely held that if there is no right- 
handed neutrino, a neutrino mass cannot be produced. This is so 
for Dirac masses. However, Maj orana masses can arise, if we have 
suitable Higgs fields. Suppose we introduce a complex, isovec- 
tor field T: 

„+ + 

(21) 

There is a unique Yukawa coupling of T to the leptons, of 
th e f o rm : 

S aa '(KLC^ l Lv,i)^* h - c - (22) 

where 

"•■(•"Hi) 

and C denotes again charge conjugation. If To takes a non -van- 
ishing vacuum expectation value, Eq. (22) yields a neutrino 
Majorana mass of the form (12), with 

M v, V ' = g w * <T°> 
Small neutrino masses can be obtained, in this case, if 

<r > « <4>o> 

Again, however, there is no natural explanation of a very 
different mass scale for neutrinos, compared to the other fer- 
mions. 

In conclusion , wi thin the standard theory, a small neutrino 
mass looks rather bizarre.lt is not forbidden , ei ther, and since 
no principle is given to compute mass ratios, even within this 
theory we must keep an open mind on this possibi li ty, as str essed 
vigorously by Pontecorvo. On the other hand, it is much too 
simple to satisfy the bounds (8) and (9) by assuming that nei ther 



130 



Vji nor T exists, so that neutrino masses vanish exactly and 
lepton flavours are conserved. It is amusing to observe that, 
in this situation, a Majorana mass is forbidden not only to all 
orders in perturbation theory, but even if we include known, 
non - pertu rbative effects, related to the iristantons. 

As remarked by 't Hooft [10], baryon and lepton currents 
in the standard theory have anomalies, and, in principle, ins- 
tanton effects may induce tiny AB^O and AL^O amplitudes. How- 
ever, it is easy to see that the current associated with B-L 
has no anomalies, so that pure AL = 2, AB=0 effects are still for- 
bidden . 



GRAND UNIFIED THEORIES 

The gauge group of the standard theory, H, may be just the 
low- energy remnant of a larger, grand unifying gauge [11-13] 
group. The standard theory in this picture should be seen as 
an approximation valid for energies much below a very large 
grand unification mass [l 4] , Mq^: 

M G(J % 10 X *GeV » <4>o> ~ 200 GeV (23) 

If this is the case, renormalizabi li ty is not a good cri- 
terion to restrict the H Lagrangian. In fact we expect the low- 
energy Lagrangian to contain all sorts of non- renormali zab le 
interactions, which represent, at energies E << Wgrr, the effect 
of the exchange of the superheavy particles implied by the GUT. 
The dimensional coupling constants of the non -renormali zable 
interactions must be of the order of inverse powers of A/gy.The 
effect of these additional terms would thus be quite invisible 
-- unless they violate some exact selection rule of the //-based 
theory. A well-known example of this is the effective interac- 
tion which is supposed to induce proton decay: 

q +q - q + I 



- 131 - 



and which appears at low energy as a four-fermion interaction, 

- 2 

with a Fermi coupling G ~(XW G y. 

It has been observed by Weinberg [15] that in the standard 
theory (with no v R and no T) there is a unique, non -renormali z - 
able coupling which could give neutrinos a non -di agonal Majorana 
mass 

f(iLc 7 'h)(%: 7 & ■ (24) 

/ is a coupling of dimension (mass) and we have dropped for 
simplicity of notation the generation indices (v>,w') of the lep- 
ton fields. After spontaneous breaking of SU(2) ® U(l) the coup- 
ling (2 4) gives rise to a Majorana mass 

M^f<4> > 2 (25) 

On dimensional grounds [16] , we expect / ^M' Gl] , or perhaps 

2 

a or a times smaller, so that 

M-(l-a 2 ) «t> Q >l/M GU ^(l-5.10-*) eV (26) 

The lesson we draw from the above considerations goes as 
follows: 

i) omitting unnecessary fields (v R ,T) we can arrange the 
low-energy theory in such a way that neutrinos stay exactly 
massless at the level of the renormalizab le couplings (which 
give rise to quark and charged lepton masses); 

ii) neutrinos can get a Majorana mass via the non-renor- 
malizable couplings induced by grand unification, on a mass 
scale completely different from the other fermions; depending 
on the features of the GUT at hand, and on the basis of Eqs . 
(24) and (26) we expect in general 

M v ^ni 2 /M GU (27) 

m being . a "normal "• mass (i.e. anything between the electron mass 
and <0o> o )- 



132 



Thus mixed neutrino masses, in the range from 0(eV) down- 
ward are predicted, in agreement with the bounds (8) and (9). 
Neutrino oscillations are in business, see Fig.l. Of course all 
this rests on the assumption that, in the GUT, amplitudes with 
AL^O, AB = [such as (24)] do indeed arise. In the rest of this 
section we shall examine two examples of GUTs to see how this 
comes about. 

i) The case of SU(5). In the minimal SU(5) scheme [12] , 
fermions of each generation are arranged into pairs of 5 and 10 
repres en ta tions : 

(28) 
10 *(u L ,d L ,u RC ,e RC ) 

[we have omitted colour indices, and neglected Cabibbo mixing; 
by introducing charge -conj ugate fields, all fields in (28) are 
left-handed] . To obtain the correct symmetry breaking we need 
two sets of Higgs bosons: one in the adjoint, 24, representa- 
tion and one in the 5 representation [which contains the dou- 
blet (16) and a superheavy colour tri plet] . Fermion masses a ri se 
from the couplings: 

01 o x 01 X 05 
06 x 010 x (4>s) + 

No neutrino mass is obtained at the level of renormaliz- 
able couplings. Such a mass could be produced by a coupling 
similar to (24), namely 

1//5X v]j E x (4> B ) (29) 

However, the coupling (29) cannot appear in the basic La - 
grangian (being non - renormal iz able ) and it cannot be generated 
by higher orders .The latter fact comes about because the minimal 
SU(5) is in fact invariant under an additional global U(l) , whi ch 
corresponds to give charges equal to 1 , -3, and -2 to 0io, 05", 



133 - 



and 6 , respectively. The coupling (29) does not conserve such 
a charge. An alternative way to see the same fact is to recall 
that, after SU(5) breaking, B-L is conserved, in the minimal 
SU(5), so that no AL/0, AB=0 effect may arise. One way of turn- 
ing around the problem would be to introduce another Higgs 
field, i.e. a 15, such that the coupling 

i//g-x xfjgx 4> 1S 

is allowed. This would be similar to (22) and it would, simi- 
larly, mess up the whole scheme. Al ternatively we may argue [17] 
that after all SU(5) cannot be the whole story. It has to be 
merged with gravity and, if gravity does not conserve any glo- 
bal U(l), then it might induce the coupling (29). This amounts 
to replacing, in Eq. (27), M GU with the Planck mass: M p 2zl0 
GeV, and we end up with the (optimistic) estimate 

M v *«fi o >l/M p ~10~ S eV 

Such masses would be relevant for solar neutrinos only. 

ii) The case of 0(10). Fermions classified in the 5 and 
10 of SU(5) can be put in a single 0(10) multi pie t[l8] - - a 16- 
dimensional, complex spinor representation --by adding a new 
neutrino field, (v R ) To break O(10) we need several Higgs bo- 
sons. Usually one starts with an adjoint Higgs multiplet, 45, 
which breaks 0(10) down to 

H' =HQU(1) B _ L (30) 

The new U(l) is coupled to B-L. At this stage, fermions 
cannot get masses. To this aim, we need to introduce a Higgs 10 
[which contains the SU(5) Higgs 5, and a 5]. When we do so, we 
discover that, because there is now a fcV, neutrinos get a Dirac. 
mass an-d, furthermore, the neutrino mass matrix is related to 
the upquark mass matrix: 

M v =tf up (31) 



- 134 



This may look like a disaster, but we have still to break 
the additional U(l) in Eq. (30). To do so, the authors of Ref.19 
propose to introduce a Higgs 126, which contains an //-singlet, 
with LfO. The effect of such a Higgs field, when coupled to the 
fermions, is to give the v R a Majorana mass. We have now both 
types of masses: the Dirac mass (31), connecting v^ to v^, see 
Eq. (2); and a Majorana mass, connecting Vn to itself, see Eq. 
(12). The neutrino mass matrix is therefore: 

M v 

T ) (32) 

M v M 12e 

where all entries are N * N matri ces (IV =number of generations) . 
If we assume Hf 12 ( >> J' v = ^| 1 .i the matrix (32) yieldsiVveryheavy 
Majorana neutrinos, with mass ~A/i2e and N very light Majorana 
neutrinos, with mass 

"light ^ M %** M V ~(M ap )*/M 12S (33) 

We have thus obtained precisely an expression of the form 
(27). In a three-generation world, the heaviest neutrino mass 
is related to the t-quark mass. By letting A/ vary between its 
experimental lower bound [20], M £, 20 GeV, and its theoretical 
upper bound [21], M t Z.200 GeV, we get 

M v ^M 2 JM 12e ^4'(10~ 3 - 10' 1 ) eV 

assuming Mi 2 e—M G r,. Notice that the latter assumption is not 
really compelling. Indeed, we learn from this example that the 
mass scale of L (or B-L) breaking, which is related to v mas- 
ses, is independent of the scale of grand unification, which 
controls the proton lifetime. The case where Mi2e is consider- 
ably smaller than Mgyhas also been studied [22], in connection 
with both neutrino and neu tron -antineu tron oscillations. 

To conclude with 0(10), it is interesting to consider an 
alternative breaking [23]. Instead of the 126, one may use a 



135 



Higgs 16 to break L, and thus B-L. When this is done, one sees 
that at the tree level no Maj orana mass is generated for v R , 
and one is led again to (31). However, as shown by Witten [24], 
the L breaking induced by the 16 propagates in any case to neu- 
trino masses. Indeed, at the two-loop level, a Maj orana mass 
for v R does arise, and we are led again to Eq. (33), with M 12e 

2 

replaced by ~<X M GV and correspondingly heavier neutrinos .Thus, 
in 0(10) we are inevitably led to small neutrino masses, the 
reason being that , con trary to the SU(5) case, the quantum num- 
ber B-L is an 0(10) generator and it must be violated at some 
level, to forbid an unseen massless vector boson. 



NEUTRINO. OSCILLATIONS SEEN? 

The experimental information on neutrino oscillations has 
already been summarized at this Conference [25]. To this, I 
should like to ad,d a brief discussion of the recent result ob- 
tained by the BEBC Collaboration, at the latest CERN beam dump 
experiment [26] . 

In this type of experiment , one observes the events induced 
by neutrinos originating from a high -density target, where the 
proton beam has been dumped. The interesting events are those 
induced by the so-called "prompt" neu trinos , i . e. those neutri- 
nos which servive after extrapolation to target o f in finite den- 
sity. The conventional interpretation of prompt neutrinos is 
that they originate almost exclusively from charmed particle 
decays. Barring unforeseen surprises, this implies equality of 
v g and v fluxes at the target, as well as equality of v and 
v^ fluxes. The result quoted by BEBC refers to the number of 
prompt -neutrino events induced in the bubble chamber with an e~ 
or an e in the final state, versus the number of those with a 
fJ. or a /x : 

N(e~) + N(e + ) 
r „_! i L—L =059±0 22 (34) 

N(fT) *N(n*) 



136 



It must be stressed that the result (34) is based on a 
small number of events, so that the evidence for R<1 is cer- 
tainly not conclusive. Indeed at the two standard deviation le- 
vel, the value R = l is compatible with observation .Nonetheless , 
it is interesting to see whether the result (34), taken within 
one standard deviation, may be compatible with neutrino oscil- 
lation, when one takes it together with the information coming 
from the other experiments. This is indeed the case, according 
to the analysis of De Rujula et al. [27] . 

To illustrate the resul ts of Ref .2 7, a few words are needed 
on the assumptions made in the analysis. 

i) One considers a three-neutrino world, where (Section 2) 
a total of six parameters describe neutrino oscillations. 

ii ) The simplifying as sumption i s made that one neutrino is 

2 2 2 

more massive than the others: m 3 >> m 1 , mq. (more precisely, 

2 2 2 2 i 2 2 i . 

m 3 - mi ~m 3 - m 2 >> |mi-m 2 | is su f fi cient ) .Only one mass thus re- 
mains, and, in addition, the matrix U loses two parameters be- 
cause of Nx,N 2 degeneracy; the oscillations de'pend therefore 
on three parameters only. 

iii) There are stringent experimental data, suggesting that 
v lJL ~' v e an d v ij ,^' 1 't oscillations are absent . Wi thin the assumption 
(ii), this can be satisfied at once with the condition: U ,=0. 

Taking (ii) and (iii), we are reduced to a two-parameter 
problem, and in fact to 'v ■«-»• v r osci llations, described in terms 
of one mass, m=m 3 and one mixing angle, 01. Figure2 illustrates 
the region of the plane m, sin 2<X which is allowed by (34) (na- 
mely R> 0.6-1) and by the reactor and accelerator data on 

P(v e -*-v g ). The most significant of the latter is the reactor 
experiment, which gives [25]: 

(Intensity of observed v ) 

- 1 — = 0.88 ±0.13 > 0.75 (35) 



(Expected rate) 
at the one standard deviation level. It can also be shown that 



- 137 - 



the values of m and sin 2<X indicated in Fig. 2 would be able to 
explain the "solar neutrino puzzle". 



20 
ST 15 

E 

10 




0.2 04 0.6 
sin (2a) 



0.8 



Fig. 2 

The shaded region corresponds to values of the V ♦*V_ oscillation 
parameters allowed by the reactor experiment (curve b) and by the 
CERN beam dump result (curve a). The figure is taken from Ref. 27. 



Finally, it is encouraging that the allowed range of m is 
well compatible with the bounds (8) and (9) and roughly within 
the region indicated by the arguments of Section 5. 



138 



REFERENCES 



[l] PONTECORVO B. , "Sot, Phys.-JETP" 26, 984 (1968); see also "Sov.Phys.- 
JETP" 6, 429 (1958) and 7, 172 (1958) 

GRIBOV V. and PONTECORVO B. , "Phys. Lett." 28B, 493 (1969) 

ELIEZER S. and ROSS D. A. , "Phys. Rev." D 10, 3088 (1974) 

BILENKY S.M. and PONTECORVO B. , "Phys. Lett." 61B , 248 (1976) 

PONTECORVO B. , n JETP Lett." 13, 199 (1971) 

BILENKY S.M. and PONTECORVO B. , "Lett, Nuovo Cimento" 17, 569 (1976) 

FRITZSCH H. and MINKOWSKI P., "Phys. Lett." 62B , 72 (1976) 

[2] For a review, see, for example, BILENKY S.M. and PONTECORVO B, , "Phys 
Rep " Ul, 225 (1978) 

[3] For recent reviews, see, for example, DOLGOV A. D. and ZELDOVICH Y. B. , 
Cosmology and elementary particles, Moscow preprint (1979) 

STEIGMAN G. , "Ann. Rev. Nucl. Part , Sci . " , 2 9, 313 (1979) 

[4] TRETYAKOV. E. F. etal., Proc. Neutrino Conf . , Aachen, 1976 (Vieweg, 
Braunschweig, 1977), p. 663 

L5J Thus a (massive) Majorana neutrino has only two states, as opposed to 
the four states of a massive Dirac particle. This has to be recalled 
when counting the number of neutrino species from the cosmological 
abundance of He, see, for example, Ref.3 

L6j This is because the complex, symmetric matrix M=S+iP can be made real 

T T 

diagonal by the transformation: M ~ , U MU , where U is unitary and U is 

its transpose 

[7] CABIBBON., "Phys. Lett." 7 2B , 333 (1978) 

L8J See, for example, E lementary particle data tables, "Phys. Lett." 75B 
(1978) 

[9] GLASHOW S.L., "Nucl. Phys." 22, 579 (1961) 

WEINBERG S. , "Phys. Rev. Lett." 19, 1264 (1967) 

SALAM A., in Proc. Eighth Nobel Symposium (ed. N. Svartholm) (Almqvist 
and Wiksell, Stockholm, 1968) 

GLASHOW S.L., ILIOPOULOS J. and MAIANI L .," Phys . Rev . " D2, 1285 (1970) 

BOUCHIAT C. ILIOPOULOS J. and MEYER PH., "Phys. Lett." 38B, 519 (1972) 

[10] HOOFT G. 't„ "Phys. Rev. Lett." 37, 8 (1976); "Phys. Rev." D U , 3432 
(1976) 

[ll] PATI J. and SALAM A., "Phys. Rev." D 10, 275 (1974) 

[l2] GEORGI H. and GLASHOW S.L., "Phys. Rev. Lett." 32, 438 (1974) 



- 139 - 

L13J For a review of grand unification, and for further references, see, 
for example, WILCZECK F. , Proc. Symposium on Lepton and Photon Inter- 
actions at High Energies (FNAL, Batavia , Illinois , 1979); GAILLARD M.K. 
and MAIANI L. , Proc. Cargese Summer School, 1979 

[l4] GEORGI H. , QUINN H. and WEINBERG S., "Phy s . Rev. Lett . " 33, 451 (1974) 

BURAS A., ELLIS J., GAILLARD M. and NANOPOULOS D. , "Nucl.Phys." B135, 
66 (1978) 

ROSS D. , "Nucl. Phys." B1U0, 1 -(1978) 

[l5] WEINBERG S., "Phys. Rev. Lett." 43, 1566 (1978) 

Ll6j An alternative way to see that / £ M -„ goes as follows. The coupling 

(24) gives rise to e +e ~* <p +<p with a pure s -wave cross-section 

2 . 2 

C ~ / •. The s-wave unitary bound is C £ E , and i ts apparent violation 

at E ~ / can be tolerated only if £ £, ^GU' wnere (24) ceases to be 
a good approximation. Arguments of this sort prove in general that the 
non- renormal izable couplings cannot exceed the appropriate inverse 
power of M (,„. 

[l7] BARBIERI R. , ELLIS J. and GAILLARD M.K., "Phys . Lett. " SOB, 249 (1980) 

[18] GEORGI H., in Particles and fields, 1974, College of Wi lliam and Mary, 
Williamsburg, Virginia, 1974 (ed. C.E. Carlson) ( AIP , New York , 1975), 
p. 573 

FRITZSCH H. and MINKOWSKI P., "Ann. Phys." 93, 193 (1975) 

[l9] GELL-MANN M. , RAMOND P. and StANSKY R. , in "Supergra vity " , Proc. of 
the Supergravity Workshop at Stony Brook, Ed. by P. Van Nieuwenhuizen 
and D.Z. Freedman (North Holland, Amsterdam, 1979), p. 315 

L20J This bound comes from the unsuccessful search for tt narrow states at 
PETRA, by various experimental groups 

[2l] CABIBBO N. , MAIANI L„ PARISI G. and PETRONZIO R. , "Nucl. Phys." B158 , 
295 (1979) 

[22] MOHAPATRA R.N. andMARSHAK R.E., Virginia Univ. Preprint , VPI-HEP-80/1 
(1980) and Proc. Orbis Scientiae 1980, Coral Gables, Florida, 1980 (to 
be published) 

[23] GEORGI H. and NANOPOULOS D. , "Nucl Phys." Bl 55 , 52 (1979). 

[24] WITTEN E., Harvard preprint HOTP-79/A076 (1979) 

[25] Se.e the talks by FIORINI E. and by RUBBIA C. at this Conference. 

[26] WACHSMUTH H . , CERN- EP/79-115 (1979), .to appear in Proc. Symposium on 
Lepton and Photon Interactions at High Energies , FNAL, Batavia, Illi- 
nois , 1979 

[27] DE RUJOLA A. , LUSIGNOLI M. , MAIANI L., PETCOV S. T. and PETRONZIO R. , 
CERN preprint TH-2788 (1979) to appear in "Nucl. Phys." B. 



- 141 - 

THIRD SESSION 
22 nd February 1980 - 9.30 a.m. 

Chairman: Leon Van Hove 



DENNIS W. SCIAMA ( * > 

THE ANISOTROPY OF THE COSMIC BLACK BODY RADIATION 

AND ITS MEANING 



INTRODUCTION 

The anisotropy and inhomogeneity of the Universe are re- 
levant to our discussions at this Meeting in two ways. First, 
these asymmetries might have an important influence on particle 
processes in the early Universe , such as pair production by the 
rapidly changing gravitational field, or the establishment of 
baryon asymmetry. Second, the presently observed rather precise 
large-scale isotropy and homogeneity may have been generated by 
these early pair production processes. Therefore any observ- 
ational information on large-scale symmetries or the lack thereof 
might be relevant to an understanding of these particle pro- 
cesses . 

The 3 K black body radiation field plays a triple role in 
this connexion. Its angular distribution acts as a tracer for 
the large-scale symmetry or asymmetry of the Universe, its very 
existence may be a residue of the annihilation products of the 



(*) Department of Astrophysics, Oxford University and Relativity Center, 
University of Texas, Austin, Texas. 



- 142 - 

9 

early pairs, and the photon-baryon ratio of ~10 may be estab- 
lished by the particle processes leading to the present presumed 
baryon asymmetry. 

It has been known for some years that the 3 K background 
is isotropic to a precision of about one part in a thousand on 
a variety of angular scales ranging from many degrees down to 
minutes of arc. This observational result has several implica- 
tions which have already been extensively discussed in the li- 
terature (for reviews see Kalckar et all 1980, Sciama 1980a, b) . 
In the last two years one anisotropy seems to have been fairly 
well established, namely a dipole variation with an amplitude 
~3 x 10 °K whose axis lies in a known direction. In addition at 
the Meeting itself the results were reported of a measurement 
of the far infra-red background (Fabbri et al . 1 980) . In addition 
to confirming the radio dipole, evidence was presented for a 
second harmonic term ~i/3 the dipole one and also for ani so tropy 
on a scale of 6° at a level ~3. ± 0.7 * 10' B . These last results 
are of great importance if confirmed. However, for the present 
we shall confine ourselves to a discussion of the dipole vari- 
ation. 



THE DIPOLE VARIATION IN THE 3°K BACKGROUND 

Early attempts to measure the dipole variation led to in- 
teresting results, but were subject to possible contamination 
from a hot spot in the radio emission from the Milky Way. One 
can avoid this contamination by working at short wavelengths 
where the non-thermal galactic radiation is substantially re- 
duced, but this requires observing at high altitudes to reduce 
the water vapour absorption. Two groups have now obtained good 
data in this way, (Cheng et al.(1979), Smoot et al. (1979) who 
give references to earlier papers). In addition there are the 
observation of Fabbri etal. in the 500-3000 micron region. Their 
results are: 



- 143 



Amplitude Right Ascension Declination 

(mK) (hours) (degrees) 

Cheng et al. 3.0 ± 0.3 12.3 ± 0.4 -1 ± 6 

Smoot et al. 3.1 ± 0.4 ii.4 ±0.4 9.6 ± 6 

Fabbri et al. 2.9 * 1.3 11. 4 ±0.7 3 ± 10 

-0.6 

The agreement between these independent measurements is 
very impressive. 



THE EARTH'S PECULIAR VELOCITY AS A SOURCE OF DIPOLE VARIATION 

The early measurements of the 3°K background already re- 
vealed its high isotropy (&T/T < 10' 3 ) (Partri dge and Wi lkin son 
1967). It was also realised at that time that this isotropy 
provided the basis of a convenient method of measuring the 
Earth' s peculiar velocity through the 3°K background, since 
Doppler shift and aberration factors would lead to a small di - 
pole variation in the temperature of the background. A rough 
estimate of our expected velocity was made in 1967 (Sciama 1967, 
Stewart and Sciama 1967), and a better one in 1968 (de Vaucou- 
leurs and Peters 1968). This subject was briefly reviewed in 
1972 (Sciama 1972). Modern estimates will be mentioned below. 

In view of the conceptual interest involved in being able 
to measure the Earth's velocity, we consider here the frame of 
reference relative to which our velocity is being measured. 
While the ultimate sources of the 3°K background presumably lie 
buried in the early Universe, and correspond to very large red 
shifts, we are more concerned here with the immediate sources 
of the background. These are to be found on the "last scatter- 
ing surface" or "cosmic photosphere" for the 3°K photons. The 
most likely scattering process is Thomson scattering by inter- 
galactic or pre-galactic free electrons. The maximum permitted 



- 144 



amount of such scattering would arise from a high (critical) 
density ionised in tergalactic gas, in which case the red shift 
of the cosmic photosphere, corresponding to unit optical depth, 
would be of order 7. The minimum amount of scattering would 
arise for a low density intergalacti c medium. In that case one 
must go back to a red shift where the background radiation (or 
QSO emission etc. ) was able to ionise all the (possibly pre- 
galactic) gaseous material of the Universe. An optical depth of 
unity would certainly be reached by the decoupling red shift of 
order 1,000, where the "3°K n background would have had a tem- 
perature ~3 ,000°K . Accordingly the velocity of the Earth which 
is being measured is that relative to the material of the Uni- 
verse at a red shift somewhere in the range 7-1000. 

It is high ly non -trivial that the distribution of matter 
in the Universe defines so well a rest- frame at each point, and 
that the actual velocities of representative portions of matter 

- 3 

deviate so little (Av/c~40 ) from these prefer red res t-frames . 
There is no sign of Lorentz (velocity) invariance here. To bor- 
row from the language of modern quantum field theory we have an 
example of a broken symmetry - not for the vacuum state in this 
case but for the actual distribution of matter in the Universe. 
I believe that is an important point, and that its ultimate si- 
gnificance has still to be dis covered. (For further comments on 
this, and in particular its possible connexion withMach's Prin- 
ciple, see Sciama 1980a, b). 

We shall now explore the plausible hypothesis that the ob- 
served dipole variation in the 3 K background does arise from 
the Earth's peculiar velocity (an alternative hypothesis will 
be mentioned at the end of this article). The Earth's net pe- 
culiar velocity would then be 350 ±60 km. sec' . This net velo- 
city is made up of a number of componen ts, of which the Earth's 
motion round the Sun (30 km. sec' ) is too small to be relevant 
at the moment. (However, it may be detectable by the proposed 
Cosmic Background Explorer satellite (COBE)). By contrast, the 



145 



Sun's orbital motion round the centre of the Galaxy is impor- 
tant (^250 km. sec ) and fairly well understood '( i ts direction 
is known and its amplitude is uncertain to ±50 km. sec' ).If we 
correct for this motion we obtain for the peculiar velocity of 
the Milky Way as a whole 

Vyy ^550 ±100 km. sec' towards galactic longitude 264° 

galactic latitude 33° 

Also reasonably well understood is the peculiar velocity 
of the Milky Way relative to the centroid of the Local Group 
of galaxies. Several solutions for this velocity have been de- 
rived, which are in good agreement with one another and cor- 
respond to a velocity ^100 km. sec . The associated correction 
is thus comparable to the error in ^uw, and we conclude that 
we can roughly estimate the peculiar velocity of the whole Local 
Group as 

v LG ^600 km. sec' 1 1-260°, b-30°. 

We now ask the basic question, is this velocity reasonable? 

(a) Comparison with observations of galaxy red shifts. 

The present situation here is so confused that it is better 
for the non-expert (like myself) to wait for better agreement 
amongst the observers. To illustrate the confusion we give here 
several recent estimates for the velocity of the Local Group 
with respect either to the Virgo cluster or to a somewhat larger 
scale distribution of galaxies. 

Peebles (1976) 250 km. sec towards Virgo 

Rubin et al.(1976) 454 ± 125 km. sec' 1 1-163°, b--ll° 

de Vaucouleurs etal.(1979) 618 km. sec' 1 1-287°, b-38° 

Visvanathan (1979) < 100 km. sec towards Virgo 

Aaronson et al. (1980) 480*75 km. sec towards Virgo 

Kjer et al.(1980) 855 ±400 km. sec' 1 1-164°, 6 --25° 

Yahil et al.(1980) 100-200 km. sec' 1 towards Virgo 



- 146 



It will be observed that the result of de Vaucouleurs et 
al. agrees well with the 3 K measurement in both magnitude and 
direction. The signi ficance of th is agreement is hard to assess 
at the present time in view of the wide range of other results. 

(b) Our peculiar velocity as a residu e o f primordial turbulence 

We now consider whether a velocity of 600 km. sec for the 
Local Group is dynamically reasonab le. One' s firs t thought, might 
be that it is a remnant of primordial turbulent velocities in 
the Universe. However, this is most unlikely because such ve- 
locities, if they are not constantly being driven, would freeze 
out during the expansion. The freezing out rate is the same as 
occurs in the adiabatic expansion of a gas, and corresponds to 
the peculiar velocity being inversely proportional to the scale 
factor of the Universe, or equivalently to one red shift fac- 
tor. Thus a peculiar velocity to-day of 600 kin. sec would have 
been relativistic at the decoupling red shift of 1000. It seems 
most implausible that the turbulence prevailing at that cosmic 
epoch could have built up undamped to a relativistic level. 

(c) The cumulative gravitational action of a density irregu- 
lari ty. 

Consider a nearby "lump" acting gravi tationally on the Lo- 
cal Group for the Hubble time of 10 years. To buildup in this 
time a peculiar velocity ^600 km. sec , the gravitational ac- 
celeration g of the Local Group would need to be given by 

r» - 1 - 2 

g ~2 x 10 cm. sec 

Such an acceleration would be produced, for example, by a 
supercluster of mass M and distance D given by 

M~10 16 M Q 
D ^30 Mpc. 

One can scale these quantities appropriately, and an ob- 



147 



vious possible culprit is the Virgo supercluster , of which the 
Local Group may be an outlying member (de Vaucouleurs 1978). 
This possibility has been analysed by White and Silk (1979) and 
White (1980). In supergalactic co-ordinates one needs to ex- 
plain a peculiar motion of the Local Group given by 

v LG ^600 km. sec' 1 L^122±7° 

In particular the peculiar motion is not directed towards 
the Virgo cluster itself, which lies at the centre of the su- 
percluster. White and Silk show that this is reasonably con- 
sistent with their dynamical picture of a flattened expanding 
supercluster. 

One might prefer to consider not the gravitational effect 
of a single identifiable supercluster, but rather that of a 
Fourier component of given wavenumber of the general field of 
density irregularities 8p/p. One would then require 

H D.— r ~ 600 km. sec' 1 , 
P 

where H is the present value of the Hubble constant, 0. is the 
density parameter P/P crit , and r is the length-scale of the Fou- 
rier component concerned. The length- scales which are most im- 
portant are determined by the spectrum of the irregularities, 
and in particular by whether &p/p r itself increases with r or 
not. This question may depend on whether yhe Universe has a high 
or a low density (Fall 1979). 

One notices also that consi derations of this kind may lead 
to an estimate of fi and so of the deceleration parameter go- 
Roughly speaking we can say that if q is small, even a sub- 
stantial density irregularity &p/p might not exert sufficient 
gravity to disturb appreciably the ideal Hubble flow. In this 
way Yahil et al. deduced from their low estimate of v, G that 



148 



go =0.02 ±0.01, much less than the value 0.5 needed just to 
close the Universe. In a similar way, the large values of v LG 
would indicate a high-density Universe. 

I f we return now to the picture of a single lump being 
mainly responsible, we would 1 ike to know whether it is a "small" 
nearby lump, or a large distant one. A possible means of dis- 
tinguishing between these cases is provided by making observa- 
tions on the angular distribution of the diffuse x-ray back- 
ground (Fabian and Warwick 1979). 



THE ANGULAR DISTRIBUTION OF THE JT-RAY BACKGROUND 

The diffuse x-ray background at energies above 2 keV is 
highly isotropic and probably comes from the Universe as a whole. 
For some time a hot intergalacti c medium has been a favoured 
source, although recently observations with the Einstein satel- 
lite (Giacconi 1980) have suggested that the background may 
consist mainly of the integrated radiation from x-ray quasars. 
In either case most of' the sources would lie in the red shift 
range ^ ~4-3, that is, much less than the red shift range 
{f 3 °K ~ 7-1, 000) of the 3°K sources. Fabian and Warwick pointed 
out that if the lump discussed above is located at a red shift 
~£ it would have a characteristically different effect on the 
x-ray and 3 K backgrounds. 

The various possibilities have been further discussed by 
Warwick, Pye and Fabian (1980), Fabian, Warwick and Pye (1980) 
and Rees (1980). One would observe somewhat different effects 
depending on whether the lump lay at a red shift which (a) is 
less than £ , (b) is comparable to fr x , (c) lies between fc and 
3->°fr< (d) is comparable to 7, ° % . Detai 1 ed calculations for these 
various cases have still to be carried out, but one can readily 
see in a general way what the differences would be. The most 
important point is the one made originally by Fabian and War- 
wick. In cases (b) and (c) the lump would induce a differential 



- 149 - 

velocity in the x-ray sources as well as in the Local Group. 
Relative to the Local Group itself this velocity field would 
possess shear, leading to a quadrupole distortion in the x-ray 
background with one axis parallel to the 3°K dipole distortion. 
Warwick, Pye and Fabian (1980) have analysed data on the 
x-ray background in the 2-18 keV range from the Leicester Sky 
Survey Instrument on the Ariel- V satellite. They obtain a si- 
gnificant quadrupole distortion whose pole at I ~245°, 6~53° 
is indeed close to the 3°K dipole axis. Unfortunately contami- 
nation by x-ray emission from the Galaxy is appreci able at these 
energies and more observations are needed before one can be sure 
that the effect has an extragal actic origin. 



AN ALTERNATIVE INTERPRETATION OF THE DIPOLE VARIATION - A LARGE 
SCALE CURRENT IN THE 3°K BACKGROUND 

An ingenious alternative to our peculiar velocity has been 
proposed by Matzner (1980). He points out that the adiabatic 
freezing out of primordial currents during the expansion of the 
Universe applies only to non-relativis tic matter. If one has 
relativistic matter.say a photon gas, then under adiabatic ex- 
pansion a peculiar velocity would remain constant .Matzner thus 
envisages a large-scale current in the 3°K background which was 
never larger than 600 kin. sec .In particular, before decoupling 
the matter would be tied to the radiation field by Thomson drag, 
and so would also then have had a peculiar velocity ~6O0 km. sec' . 
After decoupling the peculiar velocity of the matter would 
freeze out and would now be negli gible. Some of Matzner' s models 
would also give rise to a quadrupole anisotropy in the x-ray 
background. 



- 150 



CONCLUSION 

Clearly more work, both observational and theoreti cal , wi 11 
be needed before the present confused situation can be clari- 
fied. One might expect progress to be made on observational 
studies of the pattern of galaxy red shifts and with better 
x-ray data and analysis. Clearly there is a fundamental role 
here for the COBE satellite, which if successfully flown would 
transform the observational situation on the angular distribu- 
tion of the 3°K background. Far infra-red studies should also 
be pursued. In addition, there is plenty of work for theoretical 
model -bui lders . 

Altogether, we seem now to be on the threshold of estab- 
lishing fundamental data on irregularities in the large-scale 
distribution of matter in the Universe. 



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de VAUCOULEURS G. and PETERS W.L., "Nature" 220, 868 (1968) 

de VAUCOULEURS G. , in The Large Scale Structure of the Universe (ed. M.S. 
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de VAUCOULEURS G. and PETERS W.L. , to be published 1980 

FABBRI R. , GIUDI I., HELCHIORRI F. and NATALE V., to be published 1980 

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FABIAN A.C, WARWICK R.S. and PYE J.P., "Physica Scripta" 21, (1980) 

FALL S.M., "Rev. Mod. Phys." 51, 21 (1979) 

GIACCONI R. , this symposium 1980. 

KALCKAR J., ULFBECK 0. and NILSSON N.R. eds. The Universe at Large Red 
Shifts, "Physica Scripta" 21 (19&0) 



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KJER D.E. and FTACLAS C. , "Bull. A.A.S." 11, 634 (1980) 

MATZNER R. , to be published 1980 

PARTRIDGE R.B. and WILKINSON D. T. , "Phys . .Rev. Lett." U, 557 (1967) 

PEEBLES P.J.E. , "Ap. J." 205, 318 (1976) 

REES M.J., to be published 1980 

RUBIN V.C., THONNARDN., FORD Jr. W.K. and ROBERTS M.S., "Astr.J." 81, 719 
(1976) 

SCIAMA D.W. , "Phys. Rev. Lett." 18, 1065 (1967) 

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STEWART J.M. and SCIAMA D.W.-, "Nature" 216, 748 (1967) 

VISVANATHAN N. , "Proc. Astron. Soc. Austral." 3, 309 (1979) 

WARWICK R.S. , PYE J. P. and FABIAN A.C., "Mon. Not . Roy . As tr .Soc. " 190, 243 
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YAHIL A., SANDAGE A. and TAMMANN .G. A. , Les Houches Summer School 1979. 



153 



JOHN ELLIS 



(*) 



GRAND UNIFIED THEORIES AND THE VERY EARLY UNIVERSE 



1 - A. COSMIC CONNECTION? 

There has been much discussion recently about possible 
interrelations between grand unified theories [l] (GUTs) and 
cosmology. This talk is addressed to the question: Do grand 
unification and cosmology say useful things about each other? 
This is a very relevant question , since the high masses and en- 
ergies encountered in GUTs may mean that the Big Bang is the 
only place to do grand unified experiments. Listed below are a 
few of the important outstanding problems in grand unification 
and cosmology: we will see to what extent the two sides illu- 
minate the other. 

TABLE 
Some Important Problems 



Grand Unification 




Cosmology 


Fermion Spectroscopy 




Baryon Number Generation 


Grand Unification Mass n 


= 7 . 


Homogeneity and Isotropy 


Grand Unified coupling (X 


= ? 


Galaxy Formation 


SU(5) or a bigger GUT? 




Simultaneity 




G.U. Mo 


nopoles 



In this talk I will discuss briefly fermion spectroscopy, 
particularly a. possible constraint from the b quark mass on the- 
number of quarks. [2J and hence of neutrinos, which roughly 



(*) CERN - Geneva-. 



- 154 



agrees with the cosmo logical constraints discussed by Steigman 
[3 J at this Meeting. Then I will spend some time discussing the 
generation of a global baryon asymmetry in the Universe from 
GUTs L4] and the constraints this imposes on the grand unifi- 
cation mass m and coupling constant tt as well as the choice 
of GUT {SU(5)?) . Then I will discuss ideas [5] from GUTs about 
the smoothing out of initial inhomogeneti cs in the Big Bang. My 
last topic will be the production of grand unified monopoles in 
the early Universe [6]: is the number expected in GUTs consist- 
ent with cosmological upper limits? 



2 - RESULTS FROM GRAND UNIFICATION 

It may be useful to remind cosmologists of some results 

from GUTs which motivate their acceptance as plausible. One 

2 
example is the SU(2)x U(l) parameter sin 6 which gets renor- 



malized L7j from its symmetry value of 3/8 at the grand unifi- 
cation mass of about 10^ GeV to about [2] 0.20 to 0.21 at en- 
ergies -4100 GeV, because of the different evolution with energy 

of the SU(2)' and U(l) coupling constants. The present exper- 

2 
imental value of sin 6 is 0.230 ±0.015: not bad for a number 

which could have been anywhere between and J! 

A second example is the bottom quark mass, which should 
be equal to the t lepton mass at very high energies in simple 
GUTs. The ratio m.^/m. T gets renormalized above I at lower en- 
ergies L2J and the observed mass of the T implies a prediction 
of m^ ~5 to 5 l A GeV (in dramatic agreement with experiment) if 
there are only 6 quarks in total. The prediction gets increased 
by > 20% if there are 8 or more quarks, so this is phenomeno- 
logical evidence from GUTs that there are only 6 quarks, cor- 
responding to 3 neutrinos, the cosmo logi cally preferred number 
L3] . With these two phenomeriological motivations for GUTs we 
proceed to discuss. 



- 155 



3 - THE GENERATION OF BARYON NUMBER 

The universe presently contains many photons in the 3°K 
background radiation, and relatively few baryons: 

N B /N y ^10' 9±1 (1) 

Furthermore there are no known concentrations of anti- 
matter [8J - the local cluster can contain no signifi can t amount 
of antimatter, and the recently observed cosmic ray antiprotons 
[9] appear at a rate consistent with production by primary cos- 
mic ray nucleons. Before GUTs this fact (1) was often taken as 
an arbitrary condition, but now it seems possible [4] that GUTs 
may have caused an initially quark-antiquark symmetric universe 
to evolve into one with a slight quark excess, which as the 
universe cooled down would evolve into a global preponderance 
of matter as all the anti quarks annihilated. Necessary condi- 
tions for working this trick are interactions violating baryon 
number B which also violate C and CP (to allow N 4N- and a de- 
parture from thermal equilibrium of these interactions (in equi- 
librium there is no arrow of time and CP invariance guarantees 

N -N-) . 
i 1 

Important interactions in the very early "soup" include 
2*-*-2 interactions which lead to a characteristic mean free time 

3 

T^l/ncr where n is the number density of particles ~T (T is 
the temperature) and cr is the interaction cross -section : 

2 2. 

o-~0 . /T if the masses of the exchanged x particles can be ne- 

2 2 4. 

glected, much smaller a"^oi x T / m. x if m % » T. Also important are 
!•*■*■ 2 interactions which yield decay and inverse decay times 

2 2 % 2 

t ~ (T +m ) /& m (a time-dilated version of conventional free 
x decay) which -» oo as T/m -*&• This must be multiplied by a 

Boltzmann factor ~e * to take, account of the reduced den si ty 
of x particles in thermal equilibrium at low temperatures. 

The qualitative features of the mean free and decay times 
t relative to the age of the universe t are shown in fig. 1 as 



156 - 



Equilibrium for 

strong, weak and electromagnetic 




Fig. 1 

A qualitativ-e indication Ll Oj of the ratios of the expansion rate to 
mean free times for various different types of interaction. 



a function of T starting at T ^ 10™ GeV ~40 32 °K the Planck tem- 
perature. If T< t then the corresponding interaction is in ther- 
mal equilibrium. Quantum gravitational effects presumably de- 

1 9 

crease at low T and are out of equilibrium at all T < 10 GeV. 
Elementary particle interactions (strong, weak and electromag- 
netic) have t/r^a^ at 7 "~ 10 GeV but attain equilibrium at or 

2 19 15 

somewhat above T ~tx^ * 10 GeV^lO GeV. Baryon-number violating 
2*-^2 interactions behave similarly at T > 10 GeV, but then de- 
cline at lower temperatures because of a suppression due to the 
x masses £ 10. GeV in the propagators in the cross- sections. 
Baryon-number violating !•*— 2 interactions (not shown in fig.l) 
exhibit a steeper rise and fall, but also peak near T ~ 10 GeV. 



- 15.7 



Hi e -solid lines in fig. 1 correspond to processes involving gauge 
bosons, while the dashed lines correspond to Higgs boson pro- 
cesses, whose rates are qualitatively similar to those for gauge 
bosons, but somewhat more uncertain due to their less well- 
established masses and coupling strengths. We see from fig. 1 

that B-violating interactions were in equilibrium at T ~ 10 

ii 
to 10 GeV, and then went out of equilibrium, at which time a 

C-and CP -violating component could have generated the observed 

net baryon number density in the universe. 



4 - MECHANISMS FOR B GENERATION 

The dominant mechanism for B generation is likely to have 
been decays and inverse decays of superheavy Higgs H and gauge 
bosons: H <&X — q+q or q+L. The total decay rates of H and H (or 
of X and X) particles must be the same by CPT , but partial de- 
cay rates BR may differ if C and CP are violated: 

BR(X^ql) ^r f7^BR(X->qL) (2) 

which then gives a net baryon number excess 

N B 

— £ f(F-r) Z i0 _1 A r (3) 

v 



where / is the fraction of particle helicity states which are 
accounted for by X bosons. CP violation can arise in decay 
rates in 4th order of perturbation theory. 

Simple models suggest there is more CP violation in H de- 
cays than in X decays. The lowest order diagram is a minimal 
SU(5) GUT is in fact 8th order [lO] and gives 

^r-(l/10)cc 3 ( m y b M c )/ n tl^lO' 1S (4) 

which is smaller than required by (1). The Ar for X decays 
would be a factor of a smaller. 



158 - 



This is one of the problems en countered, in calculating the 
baryon number: presumably one needs a bigger GUT than minimal 
SU(5). Even SU(5) with just a few more Higgs or heavy fermion 
representations would be big enough, but the model then has too 
many free parameters to make precise numerical predictions . An - 
other complication [ll] is that one must take into account 2"*- fc 2 

FINAL BARYON NUMBER IN UNITS OF 4r 









m x dleV) 












I0O 


10 


1 


10" 


10* 








1 1 |HIM 1 1 1 




|IIIM 1 


1 1 
























\o- 4 : 


10"' 


: 








\o: 3 


\ ~ 


10-2 








\io- 2 

\l/4o\ 




v - 


irr 3 


- 


il 


Vv 10 "' 

1 1 1 ll\ll 1 1 


i.iiiu\ i i 


\,,,,.r 


"■ 



Fig. 2 

The damping effect LllJ of 2**-2 interactions on the B 
asymmetry generated by f**2 interactions for various 
different values of m (in units of 10 GeV-1 MeV) and 
grand unified coupling constants Oi . 



interactions which in fact tend to wash out the B asymmetry 

generated by l**-2 interactions. As seen in fig. 2, this problem 

is acute unless m or nt„^10 GeV and (X ^1/10: con si stent wi th 
x it x 

the preferred GUT values of m ~ 5 x 10 GeV and a ~ 1/40 .Another 
difficulty is the possibility of a complicated evolutionary 

1 5 

history of the universe. The fact that t/r«l at T > 10 GeV 
means that particle distributions may not have been in thermal 
equilibrium and some relic of this may have persisted to the 
epoch of B generation [12], giving e.g. W.^/V-. Another possi- 
bility El 33 is that the grand unified phase transition was first 
order leading to a complicated thermal history where the uni - 



- 159 



verse supercooled down to 10 GeV or so, then underwent a phase 
transition and heated back up to 10 GeV or so, afterwards cool- 
ing normally again. In such a scenario the calculation of the 
resulting B number becomes very complicated. A reasonable con- 
clusion is that we now have a qualitative mechanism for gen- 
erating the baryon number (l),but that we are not yet in a po- 
sition to make it quantitative. 



5 - THE SMOOTHNESS OF THE UNIVERSE 

The universe is now very homogeneous and isotropic, and 
the 3 K radiation indicates that it was so also at the time of 
recombination [8] . Baryon number generation calculations gen- 
erally assume that it was also homogeneous and isotropic very 

15 

early when the temperature was MO GeK.Did the universe start 
out homogeneous and isotropic, or did evolve into that state? 
As was pointed out by Misner [14] smoothing could be done by 
viscosity due to particles whose mean free path was large com- 
pared with the size of the universe, and fig. 1 indicates that 
this was likely to be true for all elementary particle inter- 
actions when T > 10 GeV. This leads us [5] to the possibility 
that "grand unified viscosity" was large very early in the Big 
Bang . 

Calculations indicate that the shear viscosity coefficient 
due to elementary particles may have been 

r) GU ^(100 to 1000) T 3 (5) 

and .the thermal conductivity 

Ku'-flO 3 to 10*)T* (6) 

where T is measured in Planck units (10 GeV £ 10 °K) . 

The large values (5), (6) would have led to dissipative 
processes very early in the Universe, and their effect on pri - 



- 160 



mordial inhomogenei ties and perturbations has been studied [5], 
It seems likely that high frequency radiative modes of oscil- 
lation (gravitons) would have been damped, as would have been 
all except very low frequency (large-scale) compressional mo- 
des. Naive calculations suggest that rotational modes of all 
frequencies would have been damped, but this is probably over- 
straining the formalism. We draw two lessons from this analysis: 
any high frequency mode likely to have caused a large fluctua- 
tion in energy density would have been damped before the baryon 
excess was developed, and very low frequency compressional mo- 
des could have remained non-zero during this epoch, possibly 
ready to evolve subsequently into galaxies as suggested by Press 
[15]. 



6 - GRAND UNIFIED MONOPOLES 

These appear [16] in gauge theories at the mass scale where 
a U(l) factor gets absorbed into a simple group, as occurs in 
GUTs at ^10 GeV . There are strong limits [6] on the GU mono- 
pole density relative to photons R from the success of nucleo- 

— 1 9 i. ' 

synthesis calculations (R&10 ) and from the present Hubble 

— 2 5 

expansion of the universe (R&10 ) .Conventional monopole cap- 
ture and annihilation rates seem unable [6] to reduce a pri - 

- io 
mordial density below about 10 ,so it becomes very important 

to estimate how many have been produced very early in the uni- 
verse . 

The basic physical process in their creation is that at 
hith temperatures the Higgs fields point randomly in internal 
space, then congealing into fixed orientations at 

T G Z 0(1) —<0\H\0>* (7) 

m H 

The Higgs field may point in different directions in dif- 



- 161 - 

ferent places, and monopoles are defects ("holes" in <0\H\0>) 
due to the incompatibility between the directions in different 
domains. Three ideas for monopole suppression have been pro- 
posed. 

Perhaps [13] the universe supercools to very low tempera- 
tures T « 10 GeV so that the separated domains are very large 
and there are relatively few "holes" between them. This could 
happen in a first order phase transition with the complicated 
thermal history discussed earlier. Alternatively, perhaps [17] 
if one calculates in a realistic model the monopoles would have 
been produced in thermal equilibrium at Tq and suppressed by a 

- m I T c 

large Boltzmann factor e 

An SU(5) calculation [14] suggests 



m „ m H /20^Ttt\ 

— ~ C- : C*0(1) x ~ 30 (8) 

T G m x \ 3 J 

which gives a sufficiently large soppression if m.a/m ^,2, as 
would for example be the case in models of dynamical symmetry 
breaking. 

Finally, some GUTs may [18] have larger monopole-antimo - 
nopole annihilation rates because the monopoles are bound togeth- 
er by pieces of weak "string" and not allowed to separate free- 
ly. I do not believe that the monopole problem is fatal for cur- 
rent attempts to combine GUTs and cosmology. 



7 - CONCLUSIONS 

There is a cosmic connection between GUTs and cosmology, 
but it is not yet clear how strong and powerful it will prove 
to be. In order of increasing speculation we have: 

- constraints on fermion spectroscopy: neutrino masses (< few 
eV) and numbers (4 3 or 4) [3] which agree with prejudices 
based on GUTs [2]. 



162 - 



GUTs provide a qualitative mechanism for baryon number gen 
eration [4]: in order for this to work we need 



m r >10 X * GeV , a ^-lO' 1 



and a larger model than minimal SU(5) . 

Grand unified viscosity may [5] have been important very early 
in the big bang: it would have permitted primordial fluctua- 
tions which could subsequently have evolved into galaxies. 

Grand unified monopoles [6] are probably not a serious cos- 
mology problem: it would be interesting to look for them ex- 
perimentally. 



REFERENCES 



[l] PATI J.C. and SALAM A., "Phys Rev. Lett." 31, 661 (1973) 

GEORGI H. and GLASHOW S.L., "Phys. Rev. Lett." 32, 438 (1974) 

[2] CHANOWITZ M.S., ELLIS J. and GAILLARD M. K. , "Nucl. Phys." B128 , 506 
(1977) 

BURAS A.J., ELLIS J., GAILLARD M.K. and NANOPOULOS D.V., "Nucl. Phys." 
B135, 66 (1978) 

NANOPOULOS D.V. and ROSS D. A., "Nucl. Phys." B157, 273 (1979) 

[3] STEIGMAN G. - these proceedings 

[4] SAKHAROV A.D. , "Pis'ma J.E.T.P." 5, 32 (1967) 

IGNATIEV A.Yu., KROSNIKOV N.V. .KUZMIN V.A. andTAVKHELIDZE A. N. , "Phys. 
Lett." 76B, 436 (1978) 

YOSHIMURA M. , "Phys. Rev. Lett." Ul , 381 (1978) 

DIMOPOULOS S. and SOSSKIND L. , "Phys. Bev." D18, 4500(1978) 

SAKHAROV A.D. , "J.E.T.P." 76, 1172 (1979) 

TOUSSAINT D. , TREIMAN S.B., WILCZEK F. and ZEE A- , "Phys. Rev." 019, 
1036 (1979) 

ELLIS J., GAILLARD M.K. and NANOPOULOS D. V. , "Phys. Lett." 80B , 360 
(1979) 

WEINBERG S., "Phys. Rev. Lett." 42, 850 (1979) 



163 - 



[5] ELLIS J., GAILLARD M. K. and NANOPOULOS D.V. , "Phys. Lett." 90B, 253 
(1980) 

[6] PRESKILL J. P., "Phys. Rev. Lett." 43 , 1365 (1979) 

[7] GEORGI H. , QUINN H.R. and WEINBERG S. , "Phys .Rev. Lett . " 33, 451 (1974) 

[8] STEIGMAN G. , "Annual Review of Astronomy and Astrophysics" U, 339 
(1976) 

[9] GOLDEN R.L. et al., "Phys. Rev. Lett." 43, 1196 (1979) 

[lO] ELLIS J., GAILLARD M.K. and NANOPOULOS D.V. - ref. 4. See also NANO- 
POULOS D.V. and WEINBERG S. , "Phys. Rev." 020, 2484 (1980) 

[ll] KOLB E.W. and WOLFRAM S. -Caltech preprint OAP-S79/CALT-68-754 (1979) 

[12] ELLIS J. and STEIGMAN G. , "Phys. Lett." 89B, 186 (1980) 

[l3] GUTH A. , TYE S. -H.H. , "Phys. Rev. Le tt . " 44 , 63! 'U980 ) ' 

EINHORN M.B. , STEIN D.L. and TOUSSAINT D. - Univ. of Michigan preprint 
UM HE 801 (1980) 

[l4] MISNER C.W., "Nature" 2*4 , 40 (1967) 

Ll5j PRESS W.H. - Harvard-Smithsonian Centre for Astrophysics preprint 
(1979) 

[16] POLYAKOV A.M. , "Pis'ma J.E.T.P." 20, 194 (1974) 

'T HOOFT G. ,"Nucl. Phys." B79 , 276 (1974) 

[l7] BAIS F.A. , RUDAZ S. and SIKIVIE P. - private communication (1980) 

[l8] LAZARIDES G. and SHAFI Q. - CERN preprint TH-2821 (1980). 



165 



GIUSEPPE C0CC0NI ( * ) 
BIG AND SMALLER BANGS SUGGESTING NEW PHYSICS 



The revolution enjoyed by particle physics since November 
1974, when the discovery, first of the neutral currents, then 
of charm, legitimized the renormali zed gauge theori es , has trig- 
gered a revolution also in cosmology. At this meeting we are 
primarily dealing with this subject when discussing proton ins- 
tability and matter-antimatter asymmetry in the early stages of 
the Universe, after the so-called Big Bang. 

In this talk I would like to consider the possibility that 
an extension of Grand Unified Theories may have something to 
tell us also about the Big Bang itself , this most peculiar, un- 
explained phenomenon that we tacitly accept as the originator 
of our Universe. 

Before coming to the arguments in support of my point of 
view, I will present a list of the most pertinent astronomical 
observations. 

1) An isotropic red shift of distant galaxies obeying the 
Hubble law 

r 100 ± 50 Kms~ Jn -n.s±o.a - i 

— = n = = 10 sec 

r 1 M psc 

2) A rather uncertain second derivative of the red shift, 
the deceleration parameter 

rr 1 

r * 



(*) CEBN - Geneva. 



- 166 



3) An isotropic background of radiation with black body 
spectrum of temperature 

T = 2.7 °K 

and consequently a density of photons in the Universe (each 
photon of ~ 10' 3 ' B eV) 

n y = 20 T 3 =400 cm' 3 . 

4) An average density of matter in the Universe 

. - 30±1 -3 

Po = 10 gem , 

and hence photon to nucleon number ratio 

n N 

5) A primeval He abundance 

He 

2: 0.25. 

H 

These facts justify a General Relativity Cosmology orig- 
inating in a Big Bang that evolves toward either' a closed or 
an open Universe depending on the exact value of the deceler- 
ation parameter, go, and on the kind of General Relativity so- 
lution preferred. 

For what follows, it is important to point out that the 
early properties of the Big Bang are independent of the subse- 
quent history of the expansion. For these early times, the Gen- 
eral Relativity equations simplify to those of the statistics 
of a high temperature mixture of bosons and fermions,a mixture 
that practically behaves as a black body boson gas. 

In co-moving coordinates, the adiabatic, isoentropic ex- 
pansion of this melange is thus described (leaving aside the 



- 167 - 

statistical weight of the various components and using cgs 
units) by the equation 

„ (3c A _i io.2 - — 

m ' * t * =40 t 2 , (1) 



\128ttGct, 

where G is the gravitational constant, o" the Stephan -Bol tzmann 
constant and t the time since the Big Bang. In more familiar 
units, Eq. (1) also reads 

1 
t 2i sec. 

(kT/MeVf 
Since the expansion is isoen tropic 

T ' r - const . 

and the radius of the Universe increases, in these early times 

as 

l 

roct 2 . (2) 

The miracle performed by the Grand Unified Gauge Theories, 
and which we here pretend to believe, is to predict that, as 
this melange expands and cools , at a certain characteristic tem- 
perature, the CP violating, time asymmetric weak interactions 
induce an asymmetry between matter and antimatter. If, e.g., 
this characteristic temperature is kT = 10 GeV , the asymmetry 
establishes itself at 

t x ^10 sec 

giving rise to the matter surplus we now observe, after the 
remaining matter and antimatter has annihilated. This means that 
the asymmetry present ly observed and responsible for 

S =-^=i0 9 



168 



is not characteris ti c of the Big Bang, but would be practically 
the same in any other Bang which is energetic enough to expand 

- 2 

as a boson gas for some time, i.e., ~ 10 sec to annihilate 
matter and antimatter and leave the baryon excess, and then 
about three minutes more to synthesize He. 

If these properties are to be common to any Bang, we are 
encouraged to look more critically at the uniqueness of the 
cosmological Big Bang. 

Most perplexing in this respect are, as others have already 
pointed out, the consequences of Eq. (2) which gives the ti 
dependence of the radius of the Universe. In fact, if 



me 



r = at 

and this relation remains valid for all values of £,then r be 
comes larger than the velocity of light when 

t < [ 

This would imply that in the very early times of the Uni- 
verse not all particles were in causal contact, giving rise to 
a paradoxical situation. 

At this point, taking the Grand Unified Theory as a guide, 
one may dare to suggest a plausible way of avoiding the para- 
dox We propose to allow the gravi tational constant G to behave 
as the other constants characterizing the strength of gauge 
fields, namely, to start decreasing when the interaction among 
particles reaches an appropriate critical energy. As justified 
later, an acceptable expression for this dependence is 



G (T) = (3) 

W77V 

where the critical temperature T should be identi fied with the 
Planck temperature 



kT. 



169 - 



*10 1B - 3 ergs =i0 19,1 GeK. 



Away from T Eq. (3) gives 



G(T) t 



T < T 



T > T„ 



G(T p /Ty 



(3a) 
(3b) 



For T<T the classical regime prevails. For T > f , sub- 



stituting (3b) in Eq. (1) 



Consequently 



Tact 



roc t 



and causality is re-established even for the smallest values 
of t. 

In order to justify Eq. (3) and the use of the Planck tem- 
perature, I will give merely a dimensional argument. (As usual 
for ultra relativistic energies, I shall employ the same unit 
for temperature , energy and mass). At the root of Grand Unified 
Theories is the prediction that, as the interaction energy in- 
creases, all particles eventually behave as points, the behav- 
iour observed at smaller energies being due to materialization 
of fields created by the breaking of a supersymmetry.lt is then 
expected that in the collision between particle, the cross sec- 
tion for deep elastic, scatterings ,i . e. , scatterings due to close 
encounters, where the four momentum transfer is greater than a 
fixed fraction of the energy involved, decreases as the square 
of the Compton wave length H/p , as it should for collisions in- 
volving only S waves. One then expects that, at asymptotically 
high energies, 




cm 



(4) 



170 - 



where Vs is the cent re -of- mass energy of the colliding parti- 
cles (in GeV in the numerical examples) and A a dimension less 
constant, not greater than about unity. 

The somewhat simplified expressions for the deep elastic 
scattering cross sections (t/s>l/2) of the four fundamental 
in teractions , so far experimentally checked only up to ^10 GeV, 
are : 

<? ED a i io- 00 - s 1 

(Electro- cr = UttCL - — = — cm 

magnetic) s (1-0. Ins) s 



a = 



/tic 1 

~ 137 



1-a In 

2 

■p 

<? CD 2 i io-* e - 3 1 

(quark- CT , t ror,g = 4770£ , tr 7 = ~ ~~ Cm 



quark) 



1+77 I 



s V 

n — 1 

0.25 J 



s t r 



s 
1 + 77 In 

2 

A 



2 

Weak G P * 

r 1 _ 38.4 2 

s cm 



(neutrinol cr m .„L = 10 

quark) Z7T s 



G p =1.05 *10~ B —2f 10' S s 

F 2 



n p 



Gravitation cT r . = inra r — = 10 s cm 



S 



^ S .,,-38.8 

a„ = — — = iO s. 



G 4ft 



c 



In the following figure these cross sections are plotted 
and extrapolated linearly up to the extreme energies. 



- 171 - 



10" 



i I 1 1 — : — i 1 I 1 1 

ENERGY DEPENDENCE OF DEEP ELASTIC SCATTERING 
FOR THE FOUR FUNDAMENTAL, POINT- UKE INTERACTIONS 




ICP 



10' 



10° 10" 



10" 



10 



20 



Notice that, apart from the renormalization correction in 
the denominator, <? ee meets, rather well, condition (4) and is 
proportional to 1/s . The same is true for °" stro „»> though the 
correction due to the renormalization of the coloured gluon 
field is larger and of the opposite sign. The meeting point of 
a ee anc ' ^strong ^ s at m x~^ GeV, whi ch determin es the proton 
lifetime and the temperature where the matter-antimatter asym- 
metry is generated. 

Radically different is the behaviour of ff , because at 

we ak 

energies below ~i00 GeV the Fermi interaction is a current- 
current interaction, and hence contains a factor 1/At <c s in 
the amplitude. This situation is expected to change around 10 
GeV (the mass of the hypothetical intermediate vector boson) 
where cr y)eak meets <x ge . Beyond that point, the coupling constant 
G- should become energy independent and cr should become 

proportional to 1/s. 



172 - 



The gravitational cross section parallels the weak cross 
section because at ul tra-rela tivi stic energies the gravi tational 
pull is proportional to the total energy of the particle, and 
hence 0L G cc.s. If this behaviour continues unabated the meeting 

s = 10 GeV, the Planck en- 
ergy. Beyond that energy, as for the weak in teraction , the cross 
section should become proportional to 1/s, the coupling constant 

2 

<Xq energy independent and consequently, G«cl/ 's^l/T . This is 
the reason why, previously, Eq . (3) was postulated as a guess 
for describing this transition. 

We are thus led to exercise our curiosity , assuming as true 
the following statements: 

i) the early history of an expanding Bang is practically in- 
dependent of the final destiny of the universe it creates; 

ii) at temperatures above the Planck temperature the gravi ta - 

2 

tional field weakens, eventually as (T /T) 

To proceed further, let us consider, not an expanding Bang, 
but the behaviour of matter inside a contracting singularity, 
a homogeneous Black Hole without angular momentum. A mass m, 
well above the Chandrasekhar , Oppenheimer-Volko f f limit, col- 
lapses and creates a closed geometry with a Schwa rzschi Id ra- 
dius 

n n m ° 
r .o = 2G — • 

c 

As the collapse progresses, in the central region the en- 
ergy density keeps increasing and when temperatures above T 
are reached, then 

G~G(T p /T)\ 

Leaving aside the serious worries about how the information 

can propagate, we propose to interpret this phenomenon asfollows: 

"the weakening of the gravitational attraction exercised 
by matter at T>T is eventually felt by all matter, even 
that at T<T p " . 



- 173 



When this happens, then the Schwarzschild radius of the 
Black Hole shrinks to a value ri < r giving to the bosons and 
fermions present in the region between r : arid r the possibility 
of leaving the Black Hole. The Black Hole evaporates, thus trans- 
forming gravitational energy back into expanding energy. 

The phenomenon here postulated would have some similarity 
to that discovered by Hawking, but would involve different 
physics and would operate on a much more grandiose scale. In 
the Hawking case, the evaporation occurs via a quantistic tun- 
nelling through r . It allows the emission of particles with 
wave lengths comparable to r itself, and consequently would be 
of importance only in the case of micro Black Holes.In the si- 
tuation here envisaged, the evaporation of the Black Hole would 
become more and more spectacular the greater the collapsing 
mass. In a comparison with nuclear physics, the Hawking process 
is similar to a emission, while the process here discussed could 
be compared to nuclear fission. In the context of General Rela- 
tivity, the bouncing back of the collapse recalls the Lemaitre 
closed solution with positive cosmological constant. 

As an example, consider a Black Hole as massive as a galaxy, 
without angular momentum. By the time some of its mass collapses 
at the centre and reaches densities beyond p "Z.10 gem' .most 
of the remaining matter has already migrated enough toward the 
centre to continue the collapse. At the rim near r , however, 
particles could eventually abandon the system. The process could 
go on until practically all matter in the Black Hole is emitted 
at higher and higher temperatures, thus giving rise to an ex- 
panding Bang. 

Having dared to go this far, let me finish with another 
odd remark. The astronomical evidence, especially that accumu- 
lated in the last decades with radio and A'-ray detectors, re- 
vealed the existence of numerous .objects that emit matter in 
the form of jets, expanding shells, relativistic particles. (I 
have in mind bodies like supernovae, radio galaxies, quasars). 



- 174 - 

Confronted with the centripetal attraction created by gravity, 
the explanation of these phenomena continues to remain uncer- 
tain and ambiguous. Could it be that the real motor of these 
expansions is a mechanism similar to the one suggested above, 
in which the weakening of the gravitational pull by matter en- 
tering the singularity, beyond the Planck limit, gives rise to 
a local Small Bang? If this were true, then in our Universe, 
besides the contribution of the Big Bang, there would be those, 
not easily distinguishable from the former, of the smaller Bangs 
created by the collapse of Black Holes. 

An estimate of the relative importance of the two contri- 
butions could be guessed as follows: assume that our Universe 
is in a steady state and its average density, p, remains cons- 
tant, notwithstanding the Hubble expansion. Then the apparent 

3 

increase of the volume V = k/3irr involves a mass increase 



dm dV 2 dr 3 r 

= p = pUrrr = pbrrr — . 

dt dt dt r 

a n O 2 8 

Since for our Universe p = 10 gem , r = 10 cm, 

F/r *n = 10 sec 

dm ..-SO,, ..1.1 ..28X3 ...17.5 .-37.8 -1 

=10 x 10 x 10 x 10 = 10 g sec 

dt 

The rate of supernovae per galaxy is ~10 y =10 sec 

34 

The mass of each supernova is ~10Mq = 10 g and there are about 
10 galaxies. The rate of total mass evaporation by supernovae 
i s th en 

dm \ is ,.34 4n - a - s 4n 37 ' s - 1 

I =10 x 10 x 10 -10 g sec 

dt / SN 

46 

Similarly for quasars: ■ the mass is ~ 10Mq = 10 g, the 
quasar lifetime ^10 y= 10 ' sec, the total number of quasars 



- 175 



> 10° and 



dm\ 



— ) =i0 6 x i0 45 x iO' 13 - 6 = 10 37 - 5 



dtj, 



Qs 



g sec 



The last two estimates being of the same order as the first 
one, indicate that a non -negligibl e fraction of matter in our 
Universe could have been processed by small Bangs, the Big Bang 
being the most important only in the hierarchy thus far known 
to us . 



177 - 



FOURTH SESSION 
22 nd February 1980 - 3.30 p.m. 



Chairman: Livio Gratton 



BERNARD J. CARR (,) 
THE ORIGIN OF ENTROPY AND GALAXY FORMATION 

1. INTRODUCTION 

Two of the chief challenges in cosmology are to explain 
the origin of the entropy in the Universe and the origiji of ga- 
laxies The entropy is contained primarily in the 3K background 
radiation and the entropy per baryon S is therefore just the 
ratio of the 3K photon number density {11^^300 cm' 3 ) to the 
baryon number density (n ft ~i0~ H cm' 3 where fl is the matter 
density in units of the critical density: P crit =3Ho/8ttG'^10' 29 g cm" 3 
for Ho =50 km s' 1 Upc' 1 ). Thus 

s ~ — ~ io B n~\ (i ) 

Understanding the origin of galaxies involves a number of 
issues but the fundamental question is how do the density fluc- 
tuations which grow and eventually bind as protogal axi es orig- 
inate. When the matter' and 3K radiation decouple at 10 s, the 
fluctuations on a galactic scale (10 M ) need to have an am- 



(*) Institute of Astronomy, Madingley Road, Cambridge, England. 



- 178 - 



pli tude 




e =[-^-1 ~ 10~ 3 (2) 



in order to bind by 10 s. One also need fluctuations on a 
larger scale in order to explain the existence of clusters of 
galaxies. 

In contemplating why 5 and e have the values they do, one 
might just assume that they were fed into the Universe as in- 
itial conditions. However, this is not a very enterprising at- 
titude, especially as it now appears possible that both para- 
meters could be explained "naturally" by processes which oc- 
curred in the early Universe and which (at least in part) in- 
volved details of particle physics. My talk assesses this pos- 
sibility in the light of recent developments. It will also in- 
dicate why the issues of entropy generation and galaxy forma- 
tion may not be entirely disconnected. 



2. THE ORIGIN OF ENTROPY 

Attempts to explain the photon -to -baryon ratio come from 
several directions. Some people assume that the excess of ba- 
ryons observed locally is global and try to explain how the 
photons could be generated in a Universe which starts off. cold 
(i.e. only with baryons and no antibaryon s) . Other people, also 
making the global excess assumption, try to explain how an ex- 
cess of baryons could arise in a Universe which was initially 
baryon -symmetric; the excess baryons would then survive after 
the other pairs annihilated when the temperature fell below 

12. 

10 K. A third group of people assume that the apparent excess 
of baryons is only local and that the Universe is globally ba- 
ryon -symmetric . In this case the problem is to explain how some 
of the matter and anti-matter managed to separate before an- 
nihilating and the value of S just reflects the efficiency of 



- 179 - 

annihilation LI ] . Most cosmologists now regard the symmetric 
cosmology as rather implausible. One needs separation on at 
least the scale of galaxies but it is very difficult to under- 
stand how this could come about [2]. Also it would seem diffi- 
cult to produce both S ^ 10 and the. observed helium abundance 
through cosmological nucleosynthesis in a symmetric Universe 
[3J. Henceforth I will therefo-re concentrate on the first two 
approaches. 

2.1 Production of photons in an initially cold Universe 

Many schemes have been proposed for producing radiation in 
a cold Universe and some of these make direct recourse to de- 
tails of particle physics. For example, the entropy could be 
generated through the decay of various species of exotic par- 
ticles which might exist at early times (such as Hagedorn's 
10 g superbaryons [4]) or as a result of a phase transition 
(such as the quark soup to nucleon transition which occurs in 
Lasher' s model [5]). Unfortunately, our understanding of such 
exotic particles and phase transitions is so scanty that it is 
difficult to make specific quantitative predictions. I will 
therefore concentrate on four somewhat different sorts of sce- 
nario. The first invokes the dissi pation of initial anisotropy, 
the second the di ssipatioh of ini ti al i nhomo gen ei ties, the third 
the production • of radiation through pregalactic stars, and the 
fourth pregalactic black hole accretion. I have selected these 
for special attention. - not because they are necessarily more 
plausible than the others - but because they i llustrate how the 
values of 5 and e may be related either to each other or to 
other cosmological parameters. 

(a) The dissipation of anisotropy . Although the Universe 
is very isotropic today, it may not always have been and many 
people have suggested that it may have started off "chaotic" 
with large anisotropics [6]. In this case the anisotropy energy 




180 



density would initially dominate the matter density and the 
Universe would be expanding at different rates in different di- 
rections. The rapidly varying curvature means that quantum me- 
chanical particle production would be important at the Planck 
time [7] 



W'^s (3) 



and the particles created could then react back on the back- 
ground and isotropize it [8]\ In this way initial anisotropy 
could be dissipated into photons and particle pairs almost im- 
mediately. Even if the initial anisotropy survived the Planck 
era, it could still be dissipated at a later time due to neu- 
trino viscosity and a host of other highly effi cient dissipative 
processes [9] . This means that most of the original shear energy 
must have gone into background radiation. However, there seems 

8 

to be no particular reason why this should produce S ~ 10 . In- 
deed these sorts of argument place an important limit on how 
much anisotropy the early Universe could have con tained, because 
if it was too anisotropic dissipation would have produced more 
background radiation than is observed [l 0] .This is a consequence 
of the fact that the anisotropy energy p a density falls off much 
faster with time than the radiation density p^: 

P a * z , p R tc z (4) 

where z is the redshift. Therefore, as illustrated in figure 1, 
even a small amount of initial anisotropy may result in a huge 
photon -to -baryon ratio today.' This line of reasoning suggests 
that the early Universe may have been "quiescent" rather than 
chaoti c [ll] . 

(b) The dissipation of initial inho mo gene i ties . If the 
early Universe contains inhomogenei ties ( density fluctuations) , 



181 




Z d ~1Q 



Fig. 1 

This illustrates why the difference in redshift dependences of p , 

Pjl and Pa puts an important upper limit on the initial anisotropy of 

the Universe. At early times the anisotropy will dominate the density 

but many processes could dissipate it into radiation at some redshift 

Zj. The generated radiation density will- eventually fall below the 

matter density and the redshift z at which it does so determines 

' -l 

the resultant photon to baryon ratio (S at z ). For example, if the 

e ' l6 

anisotropy were dissipated by neutrino viscosity at z,~ 10 (solid 

line), one could ;choose its initial value so that z ~ 10 and 

8 e ? 

S ~ 10 . However, if the same amount of anisotropy were dissipated 

earlier (dotted line), the resultant value of S would be much larger 
than observed. Since one would expect dissipative effects to operate 
at earlier times (for example, at the Planck epoch), this places an 
important limit on the anisotropy of the early Univeese. This argu- 
ment could be circumvented only if the Universe was initially baryon- 
symmetric with the baryon excess associated with the present matter 
density being generated after z ,. 



as of course are required - at least on large scales - to pro- 
duce galaxies, then there will be a continuous generation of 
entropy as these fluctuations fall within the Jeans length. This 
is because fluctuations turn into acoustical waves when they 



- 182 



fall within the Jeans length on account of pressure effects and 
the energy of these waves wi 1 1 be dissipated by the many sources 
of viscosity which operate at early times . Whenever the Universe 
has a hard equation of state (p=yp: <y4-l), the Jeans length 
is just of order the horizon size ^ct. Therefore if the fluc- 
tuations which fall within the horizon at time t then have am- 
plitude e „( t.) , the acoustical energy generated is 

P ae (t)~P~ 1 (Sp)* ~* H (*)*P(t). (5) 

This energy will be dissipated into photons and particle- 
pairs (which will eventually annihilate to produce more photons) 

- * . 

with a p= — p equation of state. If the matter itself has 

p= — p, one can see that the radiation density will always be 

2 

of order £„ times the total density. The photon -to-baryon ratio 
will therefore always be small since e ff is necessari ly less than 

1. However, if the matter has an equation of state stiffer than 

1 
p = — p (due, for example, to a strong repulsion between nucleons 

at high densities) then the generated radiation density will 
fall off more slowly than the matter density: 

p R a. z , p M tc z . (6) 

It may therefore eventually exceed the matter density (as 
is required). In this situation one can show that the largest 
contribution to 5 comes from the fluctuations which first enter 
the horizon (at time ti, say) and that it is of order [1.2 ] 

(i-3y) 

-lit! -i/ t 1 \ 2(1+y) 
S.~K Vetpjno 1 ( — j (7) 

where £i -^fj(ti) and no and Po are the baryon number density 
and energy density at the Planck time to. If we assume that the 



- 183 - 

shortest initial wavelength for a fluctuation is n and that 

the typical baryon mass is the neutron mass ~i0" g, then equa- 
tion (7) becomes 



\3v + l )el 



29\ 
S ~ 10 W r + I J el . (8) 

Zel'dovich [13] first obtained this formula for the J -= 1 
case (p=p). In this situation ti ~40 s and one generates all 
the entropy of the Universe (S ~ 10 ) if Sj. ~i0 .He claims that 
the same fluctuations on a larger scale will produce galaxies, 
so this scenario has the attractive feature of relating the two 
"fundamental" problems of cosmo logy . On the other hand, the de- 
rivation of equation (8) is questionable since it m^ay obviously 
be unjustified to assume that the wavelength of the shortest 
fluctuation is defined by the in ter-nucleon distance at a time 
when nucleons presumably do not exist. Nevertheless, in prin- 
ciple, this sort of process could generate a large value of S. 

(c) The production of radiation through stars. If the early 
Universe is cold, the equation of state will be soft after 10' s 
(before that it will almost certainly behard due to strong in- 
teractions and degeneracy pressure) and so the Jeans length may 
be much smaller than the horizon size. This means that fluctua- 
tions can fall within the horizon and bin - d (i.e. Sp/p can grow 
to 1) before they fall inside the Jeans length and dissipate. 
In this situation one expects bound regions of mass M to form 
prolifically at a time which depends on the value of e„(M) , 

t B (M)-10' s (-^-)e H (M) V, (9) 



M \ 



and these regions should produce stars (either directly or via 
fragmentation) well before galaxies form .Several peopl e [14 , 15] 
have suggested that the 3K background could be the radiation 
generated by these stars, the starlight being thermalized by 



184 



grains which are also produced by the stars. Stars bigger than 

2 

about 10 A/q are radiation-dominated and have a mass-independent 
nuclear-burning timescale [16] 



CCT n 



■MS 



UttGih, 



*10 y 



(10) 



where P is the efficiency with which they produce radiation (for 
hydrogen to helium burning ft ^0.007) and the term in brackets 
is the so-called "Eddington timescale". The resultant photon- 
to-baryon ratio is [15] 



Gm w 



— — P 



IF 



(11) 



where F is the fraction of the Universe which goes into the 

2 

stars. (If the stars were smaller than 10 Mq, t„o and 5 would 
be somewhat larger). Since the term in curly brackets is of or- 
der 1, one naturally ends up with a value for S or order 0Lq 6 
wh e r e 

2 \ 



a G 



Gm. 



he 



10 



(12) 



is the gravitational fine structure cons tan t. This pi cture there- 
fore has the attractive feature of relating the value of 5 to 
the mi crophy si cal constants. 

(d) Pregalac tic black hole accretion. One drawback of the 
last scenario is that it is not clear that the starlight really 
can be thermalized by grains. An alternative, though closely 
related, scenario invokes accretion by black holes to generate 
the 3K background [12]. The formation of pregalactic black holes 
in a cold Universe would be almost inevitable: sufficiently 
large regions could collapse to holes directly and the sort of 



- 185 



stars invoked in the last scenario could also leave black hole 
remnants after burning their nuclear fuel . Because, hoi es produce 
radiation with a greater efficiency than stars (0~0.i), they 
can produce the radiation at an earlier time t R . In general one 
needs 

t R - lO^Cl-Jfi 2 s (13) 

where fi fl is the present black hole density in units of the crit- 
ical density .Since t R can precede the time which conventionally 
corresponds to decoupling M0 s (before which the Universe is 
ionized), one can now appeal to free-free processes to thermal - 
ize the radiation. However, the value of t R is constrained very 
tightly: since fi fl <l and <0. 1 , one needs 10 ±2 s < t R < 10 13 s . It 
is striking that the first holes would indeed form in the pe- 
riod required if they were remnants of massive stars. One prob- 
lem with both the star and the black hole scenarios is that they 
do not produce the 3K radiation until after the time at which 
co smo logical production of helium and deuterium occurs ( t ^100s ) . 
Except in rather contrived circumstances, this means that one 
does not end up with the "standard" helium and deuterium abun- 
dances [17] . One has to appeal to nucleosynthesis in stars to 
produce these elements. 

2.2 Generation of a baryon excess in an initially symmetric 
Universe 

If the Universe starts off "hot", with all the present 3K 
photons, the observed baryon density (if global) would corres- 
pond to a slight excess of baryons over antibaryons at times 
sufficiently early that baryon -antibaryon pairs can be produ- 
ced. One might wonder whether such an excess could arise na- 
turally through non -baryon-conserving processes in an initial- 
ly baryon -symmetric Universe . This approach has been stimulated 
recently by the realization that baryon -non -conserving proces- 



- 186 - 

ses are indeed permi tted in the grand uni fied theori es of strong, 
weak and electromagnetic interactions (GUTS) [18-23J. In par- 
ticular, a baryon excess could be' generated through the free 
decay of the heavy Jf-bosons which characterize these theories 
and which would be abundant in the Universe at times suffi- 
ciently early that the temperature exceeded their rest mass, 
M x ^10 * -10 GeV. However, this effect is important only if the 
decay rate of the X-bosons, 

_ i_ 

r x ~ a x tfJffcV+Ajf; 2 (14) 



(where <*y is the unification coupling constant), is less than 
the cosmological expansion rate ~G (kT) when kT first falls below 
M x . Otherwise the decay and inverse decay rate is always fast 
enough to maintain thermal equilibrium and, if equilibrium per- 
tains, one can show from the CPT theorem that no asymmetry de- 
velops. The GUT scenario works therefore only if M x exceeds a 
critical mass 

M c ~ 0. X M Q (15) 

/2 1 9 

where M =(hc/G) -^ 10 GeV is the Planck mass. Whether this con- 
dition is satisfied is not clear. There are actually two types 
of J-boson, the gauge boson and the Higgs boson, and since the 
coupling constant associated with the Higgs particle is around 
10' whereas that associated with the gauge particle is around 
10' , it is probable that one must appeal to the Higgs particle 
to produce an asymmetry. Even if the Higgs mass condition is 
satisfied, the asymmetry produced (and the consequent value of 
S) is very uncertain, depending on the size of the CP violation 
involved and the details of the unification model. Estimates 
for the final value of S span a range [24] from 10 -10 , so it 
is obviously premature to claim that GUTS explains the actual 
value observed. 

It should also be born in mind that baryon asymmetries 



187 



either existing ab initio or generated before the GUT epoch are 
not necessarily erased (although this is sometimes claimed). 
The condition that GUT processes should destroy pre-existent 
asymmetries [e.g. by the two-step process ql -X -gq (where q = 
quark, q = antiquark, i=lepton) which reduces the baryon number 
by l] is essentially the same condition that it should not pro- 
duce an asymmetry (M x < M c ) . . Th e "standard" scenario [23] sug- 
gests that the initial asymmetries are first erased by the gauge 
particle (because M X <M C ) and that fresh asymmetries are then 
produced by the Hi ggs particle (because M H >M^.). However, as 



M^10 16 10 19 



10 12 -10 14 




M x 
(GeV) 



Fig. 2 

This shows how the sequence of production (P ) and erasure (E ) of 
baryon asymmetries by gauge and Higgs bosons in the GUT scenario de- 
pends upon the mass of these particles (U x and M ') . Only in the 
triangle are pre-GUT asymmetries erased and fresh ones produced, as 
the standard scenario supposes. In the lower right rectangle, pre- 
GUT asymmetries survive and may dominate the GUT-produced ones. In 
the rest of the diagram, one ends up with no final asymmetry. The 
circle indicates the region where Af_ and W„ mos t probably reside. 



- 188 - 

illustrated in figure 2, this only happens in a triangular re- 
gion of {Ma, My) space. If both M% and Mg exceed their respective 
critical masses (and it is within the bounds of possibility that 
this is the case), asymmetries existing before the GUT epoch 
may survive. Since a number of mechanisms could produce such 
an earlier asymmetry [25] ( for exampl e, quantum gravity effects 
at the Planck time [25], semiclassi cal quantum gravity effects 
- in which gravity is treated classically and particles are des- 
cribed by quantum fields - some what later [26] , primordi al black 
hole evaporations [27-29]), this is an important possibility. 
One might indeed need to invoke such effects if the GUT-generat- 
ed S turned out to be much greater than 10 . 

If, on the other hand, the S generated by both GUT and 
pre-GUT processes turned out to be much less than 10 ,one would 
have to appeal to subsequent dissipation via one of the mecha- 
nisms discussed in section 2.1 to explain theobserved value of 
5. In this case the intermediate (unboosted) value of S could 
still play an important role because of its effects on cosmo- 
logical nucleosynthesis and the evolution of density fluctua- 
tions. I will argue later that a model in which GUT and pre-GUT 
processes generate a value for S less than 10 actually has some 

8 

advantages over a model which produces «S ~ 10 from the point of 
view of galaxy formation. This raises the possibility that the 
explanation for S may involve both baronnion -conserving and di s - 
sipative processes. 



3. THE ORIGIN OF GALAXIES 

The existence of galaxies implies that the early Universe 
must have contained initial density fluctuations .Overdense re- 
gions would then expand more slowly than the background and 
eventually - providing the fluctuations were not damped out 
first - they would stop expanding altogether and collapse to 
form bound objects. To unders tand how galaxies form we therefore 



- 189 - 

need to know: (i) how the initial density fluctuations arise, 
(ii) under what circumstances they evolve into bound objects, 
and (iii) how the bound objects develop the observed charac- 
teristics of galaxies. The third question depends on detai Is of 
gas dynamics and fragmentation [30-32] which are largely inci- 
dental to features of particle physics, so I will not discuss 
it here. The first two questions, however, may impinge strongly 
on particle physics, as the following discussion will show. 

3.1 The evolution of density fluctuations 

Let us first ask what sort of fluctuations are required 
to produce galaxies. Observations indicate that the mat ter dis- 
tribution in the Universe is clumpy, not just on the scale of 
galaxies, but on all scales up to 100 Mpc. It is therefore im- 
portant to view galactic fluctuations in the context of a gen- 
eral spectrum of fluctuations which extend to much larger sca- 
les. A clue to the origin of the fluctuations may presumably be 
contained in the form of this spectrum. The form can be infer- 
red from detailed analysis of the galaxy correlation function 
[33,3 4] 

£(r)*(^-(x) ^-(x+r)S (16> 

^p p / 

which is observed' at present to be 

£ ( r yZ[— — ) (100kpc< r<10Mpc) (17) 

\10h~ Mpc/ 

where h is the Hubb le. constant in units of 50 km s~ Mpc' . The 
value of r for which £q = 1 corresponds to the scale 10 Mpc on 
which galaxies, form bound clusters- 

Because the effect of the 3K background on the matter is 
unimportant after decoupling (unless the Universe is reionized 
[35]), the matter behaves like a pressureless gas then. In these 



190 - 



circumstances simple Newtonian arguments show that matter fluc- 
tuations just increase like z until they grow to unity or un- 
til the "free expansion" epoch (z,~n _ ). One can infer that 
the density fluctuations which were present at decoupling must 
have had the form [33,341 

%.. Or)' 

where a lies between 1/3 and 1/2, depending on the value of fi. 
If fl~0.i the lower value pertains; but if ft~ 1 one has (X = % 
(corresponding to a "white noise" spectrum) and Peebles argues 
[33] that this fits the data best. The value of U^ in equation 
(18) (i.e. the scale on which fluctuations at decoupling would 
be of order unity) also depends on fi. For fi~0.1, Afi~iO Mq, 
for 0. ^ 1, Mi ~ 10 ilf©. Whi le it must be stressed that there is no 
direct evidence that the decoupling fluctuations extended down 
to the scale Mi, because equation (18) is only inferred from 
observations on scales larger than galaxies, thsre is no ob- 
vious reason why they should be cut off below a galactic mass. 
It is therefore quite possible that some regions bound well 
before galaxies and perhaps at decoupling itself. (If the Uni- 
verse was initially cold, regions- may have bound even before 
decoupling [12]). Note that galactic scales must have 
(Bp/p) dec ^10' , as indicated by equation (2). 

If we try to extrapolate the fluctuations back to still 
earlier times, we immediately face a problem because (Sp/p) no 
longer simply grow like z before decoupling. There are two rea- 
sons for this. Firstly, the rate of growth of fluctuations de- 
pends on the equation of state of the Universe. If the equation 
of state is p =yp, then fluctuations grow like 

2(l+3y) 
Kz' (1 + 3y) <ct 3 ( 1+ ?> (19) 




- 191 - 

(using a suitable gauge). After decoupling, one just has dust 
so J = and Sect . But between 10'* s (the end of the hadron 
era) and t glJ '^10 ft s (i.e. almost all the way up to decoup ling) 
the density of the Universe is dominated by its radiation con- 
tent in the standard "hot" model , so 7=1/3 and Sect. Before 10' ^ s 
the equation of state depends on details of the strong inter- 
action. In the most natural si tuation ( asymptotically free quarks) 
one would expect J =1/3 here also. However, as discussed in sec- 
tion 2 . 1 , i t is possible that a strong nuclear repulsion produces 
a "stiff equation of state during the hadron era in which case 

c 4-/3 

J = l and 8 oc t . It is also possible that the equation of state 
could go soft (as in Hagedorn's superbaryon picture [4]) and in 
this case 7=0, so S grows like t as in the post -decoupling 

epoch. Thus the extent to which fluctuations can grow before 
decoupling is very dependent on details of particle physics. 

The second reason that the evolution of density fluctuations 
is more complicated before decoupling is associated with various 
effects of the 3K background. The radiation will tend to impede 
(and perhaps reverse) the growth of fluctuations on sufficiently 
small scales. It will do this in two ways, depending on the na- 
ture of the density fluctuations. 

i) If the fluctuations are adiabat ic (in the sense that they 
maintain a constant photon -to -baryon ratio and are therefore 
fluctuations both in the matter and radiation densities), they 
will grow according to equation (19) only until they fall inside 
the Jeans length (which is of order the horizon size; see figure 
3). Thereafter, as discussed in section ' 2. Kb) , they will turn 
into acoustical waves because of radiation pressure and the am- 
plitude of these waves cannot grow again until the radiation be- 
comes decoupled at 10 s. Furthermore, below a critical scale, 
the amplitude of the waves will be reduced because of photon 
diffusion [36}. The critical scale is just the distance over 
which photons can random walk in a cosmological expansion time. 
The associated mass , ■ Mq , is the geometric mean of the horizon 



192 



lass, Mj., and the mass of optical depth unity, M T _,: 



M D ~VV*> '. M T-l(*>- 



(20) 



Since the dominant opacity before decoupling is electron- 
scattering, this gives 



M D ->10- 1B (j) l^ 



(21) 



and by decoupling this has grown to Mg^lO H M & (the Silk 

mass). Any adiabatic fluctuations on scales smaller than this 
will be exponentially damped [36] : 






M 

mI 



(22) 



Another complication is that adiabatic fluctuations bigger 
than M s but smaller than the pre-decoupling Jeans ma-is (~10 Q Mq) 
may be boosted at decoupling by kinematic effects [37]. How- 
ever, it seems likely that this boosting is just an artifact 
of assuming that decoupling occurs instantaneously [38]. In this 
case the fluctuations at decoupling would have the same ampli- 
tude for M > M S as they had on entering the horizon: 

ii) If the fluctuations are isothermal (in the sense' that 
they affect only the matter density and not the radiation den- 
sity), they will also stop growing once they have fallen within 
the horizon because of photon drag. However they will only be 
erased if they fall within the matter Jeans length. Otherwise 
they will merely be "frozen" with constant amplitude until de- 
coupling. Since the matter Jeans mass has the constant value 

_ i_ 
Af" ~ 10° 0. 2 M & (23) 



before decoupling (after decoupling .it falls; see figure 3), 



193 



M/NL 



10V 2 



13 -5/4 

10 Q 



10 o 




V 1 ° 5 W 10 ' 



Fig. 3 

This shows how various mass-scales evolve in the hot big bang model for the 
early Universe. These scales play a crucial role in determining the evolu- 
tion of density fluctuations. M^ is the horizon mass (including the mass of 
the radiation content; this will dominate that of the matter content before 
* e .)- Until a fluctuation falls within the horizon it cannot be affected 
by any causal processes like viscous dissipation and photon drag. It , is the 
total Jeans mass (including the mass of the radiation content). This spe- 
cifies the scale below which pressure effects are important. The radiation 
pressure always exceeds the matter pressure until decoupling; this means 
that M, is of ordur M„ until t and that it flattens off between t and 
t dec ( t cq < f de c ** ** > 0.1). When an adiabatic fluctuation falls within M ,, 
it will be converted into an acoustical wave. M, is the matter Jeans mass; 
this specifies the scale below which matter pressure is important and it 
plays a similar role for isothermal fluctuations as It, does for adiabatic 
ones. It j is constant before t Jec ; after t, , when the radiation decouples 
from the matter and no longer impedes the growth of matter fluctuations , the 
total Jeans mass drops to the value M.. W fl is the mass below which adiaba- 
tic fluctuations are erased through photon diffusion. The value of U n at 
decoupling, the "Silk" mass (M s ), specif ies the scale above which adiabatic 
fluctuations can survive the radiation era. 



- 194 



all isothermal fluctuations on scales larger than this will sur- 
vive and begin the matter era with the amplitude they had when 
they first fell within the horizon. No te, however, that for iso- 
thermal fluctuations one must distinguish between the fluctua- 
tion in the total density, p T , and the fluctuation in the mat- 
ter density, /0„. Since 



Sp/p 



(6p/p) 




Mj m (t eq ) 



-»iVI 



M s M j(W 



Fig. 4 

This shows the relation between the density fluctuation when a mass-scale 
M falls within the horizon (Sp/p) „ (solid line) and the matter fluctuation 
it produces after decoupling [Sp/p) ^ (broken lines). Fluctuations in the 
radiation density (adiabatic fluctuations) are erased on scales below M„ by 
photon diffusion. Fluctuations in the matter density (isothermal fluctua- 
tions) survive on scales larger than the matter Jeans mass at decoupling. 
In both cases , for M < U„(t g ), the surviving scales have (Sp/p)^ (Sp/p) 
providing one interprets (Sp/p) in the isothermal case as the fluctuation 
in the matter density alone. Tliis is because the fluctuations stop growing 
between falling within the horizon and t either because of radiation pres- 
sure in the adiabatic case or because of radiation drag in the isothermal 
case. For M~>M„(t ), both sorts of fluctuations will be boosted by a fac- 

2 /S 
tor ( t i ec / t eg ) . providing '^.^ 'dec' " account of the flattening of the 

Jeans mass between t and t, 

e q dec 



195 - 



the fluctuations do not have the same form. In parti cular, since 
a matter mass M falls within the horizon at a time t ff <* M 
during the radiation era, the total horizon fluctuation is re- 
lated to the matter fluctuation at decoupling by the equation 

(-—) cl(-) *M~*M°' a (25) 

V Pj T ,H \ P/M,dec 

where a is defined by equation (18). 

The evolution of M H , Mj, Mj and M D is shown in figure 3 
and the relation between the horizon -sea le and decoupling fluc- 
tuations is illustrated in figure 4. In the conventional "hot" 
scenario, the fact that Mg is larger than a typical galaxy mass 
(and more comparable to the mass of a cluster of galaxi es ~i0 M~.) 
suggests that, with adiabatic fluctuations, galaxies could only 
form by fragmentation: that is, the 10 Mq regions have to bind 
first and then fragment into galaxies [40]. On the other hand, 
with isothermal fluctuations, the smallest surviving fluctua- 
tions would bind first and then ever larger units would form by 
hierarchical clustering. Exactly what singles out a galaxy as 
the smallest scale on which structure persists in this model is 
not clear - although various gas dynami cal arguments are fairly 
plausible [32] . 



3.2 The origin of the density fluctuations 

We have extrapolated the fluctuations required to make 
galaxies back until the time at which they first fall within 



>8 „ ,, ,„12 



c ■ 



the horizon (t#~40 s for M ^ 10 tf). Before this time theflu 
tuations are larger than the horizon and are therefore not sub- 
ject to any of , the causal dissipative effects described in the 



196 - 



last section .They merely grow due to gravitational instability 
in the manner described by equation (19). The question now, 
therefore, is where do the hori zon - scale fluctuations come from? 
Ideally one would like to be able to show that the fluctuations 
could arise spontaneously at. some time and then grow to have 
the value required at t^. Unfortunately, i t has pro ved very dif- 
ficult to explain how the required fluctuations could arise in 
this way and most cosmologists have therefore concluded that 
the fluctuations just have to be fed into the initial conditions 
of the Universe (i.e. at the Planck time). This is hardly a sat- 
isfactory attitude since it means tha t, ultimately, one has more 
or less given up hope of explaining the origin of galaxies. 

However, the situation is not completely hopeless. One pos- 
sibility is that the fluctuations were induced by quantum gra- 
vity effects at the Planck time [41]. Harrison has suggested that 
these will naturally endow the Universe with initial fluctua- 
tions of the form [42] 



(26) 



where e^ is a constant (0<Sg<l) and M is the horizon mass 
at the Planck time ^10 g. These fluctuations have the attrac- 
tive feature that they have always grown to a scale invariant 
amplitude e ff on first entering the horizon (independent of the 
equation of state) .Various people [7,39] have argued that such 
"constant curvature" fluctuations are just what is needed to 
produce galaxies and clusters of galaxies. In particular, 
Zel'dovich has argued [7] that, if e^~iO , one can produce 
both the photon to baryon ratio (via the dissipation of small 
scale fluctuations discussed in section 2.1(b))and the observed 
large scale structure of the Universe. On the other hand, the 
argument that quantum gravity effects produce density fluctua- 
tions of the form (26) is far from convincing, so one should 
also seek other natural ways of producing density fluctuations. 




- 197 - 

It has recently been suggested [43,44] that the required 
fluctuations could arise in an initially homogeneous Universe 
through purely statistical effects if the Universe was ever 
"grainy". Of course, at some level, the Universe is bound to 
develop graininess since we know that (at sufficiently late 
epochs) the matter will be in discrete particles like protons. 
However, it is well known that. grains of only 10~ gm are far 
too small to produce galaxies through statistical effects. On 
the other hand, graininess might develop on much larger scales 
whenever the Universe undergoes a phase transition . Such a phase 
transition might occur, for example, at the GUT unification era 
[45] , at the nuclear density epoch [46], when the superbaryons 
decay in Hagedorn' s model [4], at the atomic density epoch in 
a cold Universe [47, 48], or when the quarks belatedly fuse into 
nucleons in Lasher's model [5]. In all these situations one ex- 
pects grains of a specific mass M* to form at a specific time 
t*. 

In estimating the size of such statistical fluctuations, 
one must bear in mind that one is interested in fluctuations 
on scales initially much larger than the horizon (on scales 
containing N grains, say). It is quite unrealistic to appeal to 
the usual V^V effect on such scales since there has not been time 
for the grains to randomize their positions; and anyway one can 
show that such fluctuations are not really meaningful since they 
would close the Universe on a sufficiently large scale [49]. If 
one assumes that grains can only randomize their positions on 
scales less than the horizon size, one would naively infer in- 
itial "surface" fluctuations of the form 

_) * M 3 . (27) 

P I* 

However, one can show that this is wrong (because equation. 
(27) gives the fluctuation in the number of grains but not in 
the total energy) and that the "effective" density fluctuation 
is really [50, 5l] 



198 




(28) 



Fluctuations of this form are inevi table and although they 
are much smaller in amplitude than those described by equation 
(27), they can still be significant. For example, if the fluc- 
tuations on a matter scale M originate and fall within the hor- 
izon during the radiation era (when p =p/3), one finds [43] 





(29) 



- 7/ fi 

Note that, although the fluctuations go like M~ at t* , 

- 1/2 

they turn into M ' fluctuations at decoupling because of their 
growth before falling within the horizon at tu<£.M .It is in- 
teresting that such a "white noise" spectrum of fluctuations is 
just what Peebles argues is requi red to explain the galaxy cor- 
relation function [33]. 

Un fortunately , in the standard "hot" model, the statistical 
fluctuations described by equation (29) are not large enough to 
produce galaxies and clusters. For since causality requires the 
grains to be smaller than the horizon at t«,and since galactic 
scales need (Sp/p) dec to be about 10~ , we require t*>10 s and 
it is hard to see how a phase transition could occur as late as 
this in a hot Universe [44] . However, if the photon -to-baryon 
ratio had an initial value S much less than its present value 
(i.e. if the early Universe was " tepid" or "cold" - a possibili- 
ty discussed in section 2) , the statistical fluctuations could 
continue to grow even after falling within the horizon because 
the Jeans length would be very small (see figure 5). In this 
situation ($P/ P) j e c could bemuch larger than indicated by equa- 
tion (29). If the photon -to-baryon ratio is boosted to its pre- 
sent value at a time t R one finds [43] 



- 199 - 




■10' 



M 



,10 12 M Q 




(30) 



3 could probably only be boosted at very late times by 
black hole accretion and, in this context, we saw in section 
2.1(d) that t R has to be around 10 % in order to satisfy en- 
ergetic and thermalization criteria. One also requires S to ex- 
ceed 10 in order to avoid over-producing helium through cos- 



M 



NIj(t eq ) 



Mi 




» t 



*rec *R *dec 



Fig. 5 

This illustrates various evolutionary features of a Universe which 
starts off with a photon- to-baryon ratio Smuch less than 10 , the extra 
photons being generated at some time t fl . The Jeans • mass M, is of order 
the horizon mass U fl until the matter and radiation densities become 
equal at t ^ 10 S s. Thereafter it remains constant at 10~ S M a until 
recombination at t rec ^10 S s when it-drops to 10 Sll Q , After t R , Uj 
evolves as in the standard model. Because t „ cannot much precede de- 

13 

coupling (r dec ~f0 s) in the suggested scenario, the period in which 
Mj is flat is generally very long and this means that bound systems can 
form very easily then. 



- 200 - 
mo logical nucleosynthesis [173. One infers that galactic scale 

— 3 —A- 

fluctuations could be as large as 10 providing t * > 10 s. In 
fact, in a tepid Universe, 10 s ( the end of the hadron era) is 
really the last time one could expect a phase transition to oc- 
cur. If such a transition does occur then, and if it produces 
horizon-size (~ IMq) grains, one does indeed anticipate the sort 
of galactic scale fluctuations required providing S is not much 
larger than 10 . The same statistical fluctuations (on a smal- 
ler scale) could produce the pregalactic black holes which are 
required to generate the extra radiation L43J . However, one no 

- 1/2 

longer has ($p/p) dec <cM 

The possibility that the early Universe was tepid high- 
lights another way in which particle physics could affect our 
picture of galaxy formation: via its possible determination of 
the initial entropy parameter .Thi s is because the two important 
mass-scales which arose in the discussion of section 3.1, the 
matter Jeans mass and the photon diffusion mass at decoupling, 
both depend on S: 

Mj ~ 10 S*M 9 , M s ~ 10 3 S*M Q . (31) 

If the mechanisms discussed in section 2 produced an in- 

8 . 

itial value for S less than 10 , these characteristic masses 
could be much smaller than their conventional values. Ihis would 
circumvent one of the prime problems in explaining galaxies. 
For if the present photon -to -baryon ratio was primordial or gen- 
erated in one step, the Silk mass would exceed the mass of a 
galaxy and so, if the fluctuations were, adiabatic (as they would 
have to be in the GUTS scenario), galaxies could only form via 
fragmentation. This is embarrassing since the fragmentation 
scenario faces severe theoretical difficulties [52] . However, 
if the present photon -to -baryon ratio was generated in two steps 
(e.g. first by GUTS and then by black hole accretion), this 
problem would be averted since adiabatic fluctuations could 
survive and become bound before the- value of S was boosted to 



- 201 



its present value. 

The evolutionary features of a tepid Universe are shown in 
figure 5. The crucial point is that the Jeans mass no longer 
goes like the horizon mass all the way until decoupling but 
flattens off after the radiation density falls below the mat ter 
density (cf. figure 3). This means that bound systems can form 
very easily then [533. These bound systems will either collapse 
directly to black holes or fragment into stars which may them- 
selves collapse to black holes after the nuclear burning time- 
scale ty S . For massive stars ty S ^10 s , f rom equation (10), so 
the resultant holes form just at the time required to boost S 
to 10 , as described in section 2.1(d). One would expect these 
holes to cluster because of the statistical density fluctua- 
tions discussed above. If galaxies form out of the gas which 
sinks to the centres of the cluster potential wells, they would 
therefore be born with a halo of black holesjand in ri.ch clus- 
ters of . galaxi es one would expect the individual members to be 
tidally stripped of their ho les , leaving a collective black hole 
halo [54J . The black holes which boost the value of S in the 
tepid scenario would therefore be natural candidates for the 
"missing" mass in galactic halos and clusters. 



4. CONCLUSION 

We have seen that the origin of both the photon -to-baryon 
ratio and galaxies may depend crucially on details of particle 
physics. Whether one tries to explain the value of 5 through 
dissipative processes in a cold Universe or through the gener- 
ation of a baryon. excess in an initially symmetric Universe, 
some recourse to particle physics may be necessary; and particle 
physics affects our picture of galaxy formation both by deter- 
mining the equation of state at e'arly times (which in turn de- 
termines the growth rate of density fluctuations) and by its 
possible generation of the fluctuations themselves .We have also 



2 02 



seen that the origin of the photon -to -baryon ratio and galaxies 
may not be entirely disconnected issues, since some scenarios 
explicitly relate S and e. Furthermore, several problems of ga- 
laxy formation would be al leviated if S was initially less than 
its present value. 



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205 - 



CARLO RUBBIA ( * > 



EXPERIMENTS WITH ELEMENTARY PARTICLES RELATED 

TO COSMOLOGY: NEUTRINO OSCILLATIONS 

AND PROTON LIFETIME 



ABSTRACT 

Several experiments which relate to neutrino mass and oscillations are 
reviewed with special relevance to cosmic ray and reactor results. Some of 
these experiments are suggesting the existence of neutrino oscillations, 
which in turn imply neutrino rest masses. The existence of tiny neutrino 
rest mass if confirmed will have significant consequences in cosmology . 

The states of the search for proton instability is also reviewed. If 
this process will be detected at the level predicted by current theoretical 
ideas, it would provide a key to the understanding of the early "phases of 
big bang and to the creation of matter. 



1. EXPERIMENTS WITH COSMIC RAY NEUTRINOS 

1.1 Introduction 

Properties of neutrino interactions with matter are well 
studied by accelerator experiments up to an energy of about 
200' GeV. These experiments have been extensively discussed in 
the report by Fiorini at this Symposium. Cosmic ray experiments 
cannot compete with the rate and completeness of information 
events in bubble chambers and similar devices used at acceler- 
ators. However there are two main reasons which make cosmic ray 
experiments uniquely interesting: 

(i) the distance between the. detector and the source can 
be as large as 10 kilometres and thus the experiments with cos- 



(*) CERN, Geneva. 



- 206 



mic ray neutrinos have sensitivity to neutrino oscillations LIJ 
which cannot be realised in. the laboratory. For more details 
on the question of neutrino oscillation we shall refer to the 
paper by G. Maiani, at this Symposium. Assuming for simplicity 
mixing between two kinds of neutrinos, the flux of neutrino be- 
comes modulated in time according to the expression: 

I(p,l) =I(p, 0)11-1/2 sin 2 2®(l-cos 2rrl/l )] 

2 

where ® is the mixing angle and lo=2.U7 p/Am is the oscilla- 
tion length in metres between two neutrinos of momentum p 
(GeV/c) and of masses mi and m? in eV. Note that in general one 
would expect three masses and three mixing angles. For <p> ±10 

4- 2 2 2 - 3 2 

GeV and lo—10 Km we find Am = m 2 -m t ^10' eV . If accelerator 
or reactor experiments would confirm preliminary evidence for 
oscillations on much shorter flight paths , for cosmi c ray s l»lo 
and the cosine term will average out. The observation of an at- 
tenuation of the flux will then give a clean measurement of the 
mixing angle: 

I(p, I » lo) »I(p, 0)11-1/2 sin 2 2®] 

As well known, the apparent lack of flux observed by the 
solar neutrino experiment which is sensitive to Am ^ 10 eV, 
could be due to such a mixing effect. 

(ii) The cosmic ray detectors could observe extra terres- 
trial high energy neutrino sources of astrophy sical origin. For 
instance a source in our galaxy will be detectable by the lar- 
gest detectors under construction provided its neutrino lumi - 

4 

nosity exceeds 10 erg/sec. Possible existence of such sources 
can be related to supernova explosion [2]. In turn a single of 
these explosions could provide a fantastic time-o f- flight meas - 
urement for few eV neutrinos over galactic distances , thus giv- 
ing information on their mass and oscillations [3j. 



- 207 



1.2 Expected fluxes of cosmic ray neutrinos 

Neutrino are produced by the decay of particles produced 
throughout the athmo sphere by cosmic ray cascades. At low en- 
ergies the bulk of the spectrum is due to (K) tt + -fi + +v and 
M ~ >e +v e +",„ decays, leading to v mu , v g in the ratio of ap- 
proximately 2 :1. The spectrum is easi ly related to the observ- 
able /x-flux and /J. /jjT ratio which are well known. Therefore in 
principle these neutrino fluxes can be predicted. At high en- 
ergies there could be a "beam dump" component due to decays of 
short lived particles, like charm or higher flavours provided 
their production cross -section becomes significant. It is in- 
teresting to notice that the well known sec® zenith effect could 
be used in principle to separate the two sources (just like in 
the classic case of the muon flux). 

1.3 Early experiments 

The simplest experiment to detect neutrino events under- 
ground is the observation of underground muons at sufficient 





I I ' 1 1 1 1 1 


o 32 


^Atmospheric 


to 

c 


/ \ muons 


</> 24 


: in 


h 


■£ 


r 1 


\L 


2 
a> 


■ J 


u n 


- 


T5 16 


T \^ 


- 


Number 

00 

n=cn 1 1 — 


l 

i i j — i- 


i Neutrino-induced 
V muons 



20 40 - 60 80 

Projected zenith angle (degrees) 



Fig. 1 



208 



depth in order to ensure that most atmospheric muons have been 
stopped. The huge matter around the detector is the effective 
target and the long range of the muon from v enhances the 
rate and permits detection with a relatively modest detector. 
These experiments are very etude since they have no energy re- 
solution and the reaction vertex is hidden from the detector. 
However they have led to significant results and to the obser- 
vation of the effect, roughly at the expected level: 

1) The Kolar Gold Field [4] experiment has operated during 

2 

the period 1965-1969 with hO m of slabs of plastic scintilla- 
tors and Conversi flash tubes at a depth of 7 10 gr/cm . Their 
result is shown in Fig.l. One can see that in addition to sur- 
viving muons from cosmic rays there is a component, presumably 
due to neutrinos at large zenith. The "anomalous tail" contains 
16 even ts . 

2) The Case Withwatersrand [5] experiment run during the 

2 

period 1964-1977 with 160 m of liquid scintillator slabs and 
Conversi flash tubes at a somewhat greater depth of 8. 7 10 gr/ 
cm . An improved version of this experiment [6] including Uni- 

.2 

versity of California at Irvine (CWI) with i74 m of liquid 



c 

3 

o 
o 



£ 

3 



20 


i 1 1 1 1 1 '"- t — 7-1 — 








n 


Moximum -likelihood s 




10 




r 


\ 




- 




- / 


\ — ~^ 

V-^^Fit z/-produced muons - 




rr^ 


' - — N- — Atmospheric muons 

-i 1 ■ r- — it* 



20 40 60 

Zenith angle 8 (degrees) 



80 



Fig. 2 



209 - 



scintillators and Conversi tubes has collected data during the 
period 1967-1971. In total over 110 neutrino induced events have 
been recorded, showing a very clean separa tion between penetrat- 
ing muons and neutrino induced events (Fig. 2). 

We can combine both experiments in a curve showing the flux 
of muons as the function of the actual depth to be traversed 
from the surface at the observation angle (Fig. 3) . One can see 
then a very clean separation between the very rapidly falling 
event rate due to surviving atmospheric muons and a long, cons- 
tant plateau due to neutrino induced events. 

Fluxes observed by the two groups are given in Table I. 
We can conclude on a reasonable agreement between these obser- 
vations. It is interesting to compare these results with the 
predictions of an integration over the neutrino spectra and neu - 
trino cross-sections. A very striking feature of these experi- 
ments is that the decrease of the neutrino flux with energy is 
almost exactly compensated by the rising of the neutrino cross- 
section and the increase range of the muons, For instance events 
due to neutrino < 1 GeV and > 1000 GeV both contribute to about 
10% of the observed muon flux. The calculated flux, based on 



o 
<u 
in 

CM 

'e 



CW I COLLABOR. 



1 10" 



10 



oV 



- 10 



H2 



^ 



10 



*I3 



Atmospheric muons 






ll 



\ 



H-H 



-]_ 



_i_ 



6 K) 20 30 40 50 

Slant depth in units of 10 gr/cm 2 
h= h_ sec Q 



Note scale change 



• Neutrino induced muons 
-I 1 1- 



60 |I60 I 

200 



1160 

D 



Fig. 3 



210 



TABLE I 
Muon flux, cosmic ray neutrino associated (Horizontal) 



Group 


2 

(Depth gr/ cm. ) 


-2-1 -'l 

Flux (cm s sr ) 


4) 
KGF 

e) 
CWI 


5 

7 10 
8.9 10 B 


(3.5 ± .9)10' 13 
(U.59 ±0.42)10~ 13 



neutrino fluxes and accelerator neutrino cross - section is (7±1 .8) 
10 cm s sr somewhat smaller than what observed. Taking 

the average between the two results and comparing with calcu- 
lations, we get: 



measured h . 37 ±0.38 



predicted 7.5 ±1.8 



0.58 ±0.148 



corresponding to a missing flux of (3.13*1.84) 10' 13 cm' 2 s' 1 sr' i , 
or about two standard deviation effect. Can this anomaly be due 
to neutrino oscillations? To compare different experiments it 
is convenient to introduce a reduced distance X. between sources 
and detector defined as: 

distance from source, metres 

K = < ! ■ > 

neutrino energy, IHeV 

The average value for these experiments is k = 50 m/MeV. 
It must be remarked that in these experiments, since muons are 
travelling almost horizontally, the traversed amount of mate- 
rial is far less than the earth diameter. 



1.4 Observation of neutrino across the whole earth 

A very interesting new experiment [7] has been able to se- 
parate clearly upward and downward muons emerging from the rock 
by a time of flight technique . The apparatus (Fig. 4) located in 



- 211 





Fig. 



Baksan Valley, North Caucasus consists of 3132 liquid scintil- 
lators arranged in a semi-cubic geometry of 16x16x11 m . In 

4 2 

spite of the very shallow depth (8.85 10 gr/cm to the closest 
surface, (to be compared for instance to 8.9 10 gr/cm for the 
CWI experiment) the upward rate, even if 10' smaller than the 
downward rate, can be clearly separated (see Fig. 5). The events 
are interpreted as due to neutrinos traversing the whole earth. 
So far about 30 single muon and one di -muon have been record- 
ed L8J , at a rate in perfect agreement with the expected flux 



290 



m 5-6 



-2.0 



-IS 



njl 

-1.0 



N 

500 

200 
100 
50 

20 

10 

5 

2 

I 




2.0 



Fig. 



- 212 



and no neutrino oscillations. The experiment is presumably at 
\ = 600 m/MeV. 

A word of caution should be stressed of this point. Not 
only these results are very preliminary and unpublished, but 
also their in terpre tai on could become somewhat more complex if 
oscillations were to be affected by coherent interactions [9] 
with the matter of the earth, in analogy with /fi-#2 regenera- 
tion. In other words, oscillations might be confused by regen- 



eration 



2. COMPARISON WITH EXPERIMENTS IN THE LABORATORY 

2.1 Accelerator experiments 

Several accelerator experiments have looked for transi- 
tions between different types of neutrinos. For more detail we 
shall refer to the paper by E. Fiorini at this Symposium. In 
short: 

(i) at CERN , the Gargamelle Collaboration [10] has looked for 
v —v transitions (and found no evidence); 

(ii) at Fermilab, in the 15 bubble chamber, reaction leading 
to transition v ~*-v . has been searched but .not found 
[11]; 
(iii) Some anomaly in a beam dump experiment could be attribut- 
ed [12], although not unambiguously, to v e ~*~ ~ >v tau tran- 
sitions; 

(iv) Comparing cross -section measurements at the CERN PS and 
CERN SPS which have different length of neutrino beams, 
gives some information on v_„ — v transitions. 

(v) At the Los Alamos pion factory, neutrinos from decays of 
stopped pions have been observed, giving information about 
absence of v —v transitions. 

Bill C 



- 213 - 

TABLE II 
Neutrino oscillation experiments vith accelerators 



Reaction 


Reduced path, 
m/MeV 


k 


Results 


Remarks 


v—v 


v—v 


V^V 


0.025 




-0.03 ±0.1 


0.02 ± 0. 07 


10) 
GGM/PS 


V ^ V r 


0.040 




< 0. 025 


- 


11 ) 
FNAL/15'BC 


V — V 


0.1 




1 ±0.07 


1 ±0.1 


Match-SPS 
and PS CR 95.5 


V- e 


0. 1 








Los Alamos 

no evidence to 

Am^-1 eV 



All results are listed in Table II, as a function of the 
reduced decay path A.. Note that these numbers can be combined 
and give an estimate of a limit to oscillations of v into 
neutrinos other than v g and ^ tau , using the unitary condition: 

p ( v »u~ v » a ) +P (v* a ~ v ) + p ( v * a - v tau) '0,97 ±0.12 

Not much room is then left at this point for oscillations 
into undetectable neutrinos, partners of massive charged lep- 
tons still to be discovered. 



2.2 Experiments with reactor neutrinos 

Hie V g flux at distances of 6 m and 11.2 from the reactor 
core centre were measured by Reines et al. [l3l. The detector 
consisted of 45.7 Kg of plastic scintillator surrounded by a 
300 Kg of Nal shield. Using the known cross-section for the in- 
verse beta decay reaction v p — e n and the calculated neutrino 
spectrum from the reactor one can -get informations of the pre^' 
sence of neutrino oscillations. The measured fluxes at 6 m and 
11.2 m are shown in Fig. 6. One can see that the Davis spectrum 
[l4] seems to accomodate the data. Results are definitely below 



- 214 - 



c 

3 



-O 

v- 
D 



1^ 



I I I 1 1 I — - 

Avignone 1978 

Oovis 1979 

•Carter 1959 




L=6m - 



Avignone 1978 

Davis 1979 

Reines 1978 




E,-; (MeV) 



Fig. 6 



the estimates of Avignone [l 5] . This discrepancy , i f real, might 
be interpreted as due to neutrino osci 11 ations . In the simplest 
analysis of two neutrinos oscillating with length \=K /E E and 
mixing angle $ we expect that intensity of neutrino to be mo- 
dulated with the simple law: 

sin v$ f" / E v \~\ 

The data expressed as ratio between observed and expected 
fluxes L 16 ] are shown in Fig. 7. One can see that perhaps there 
is suggestion for oscillation pattern with a node in the range 
covered by the experiment. The indicated fit through the data 
is P(v e ~~v e ) =1 +0.44 sin (1.27 L/E) corresponding to a mass 

2 

difference of about 1 eV .A very recent paper by Reines et al. 
[17] removes the basic uncertainty of the knowledge of the neu- 
trino spectrum. In the new experiment the detector made of 268 Kg 



215 




_. 1.0 
t 
a. 0.5 



-<P> 



Avignone 1978 spectrum 




TO 



^ 




J_ 



f 



■ L=11.2m 
• L= 6m 



-<P> 



12 3 4 

L/E (m/MeV) 

Fig. 7 

of D 2 is exposed to the neutrino flux from the same reactor. 
Immersed in the DqO there are He filled neutron proportional 
counters. The D 2 target is enclosed in lead and cadmium shield 
and surrounded by liquid scintillator anticoincidence counters. 
This detector is capable of observing not only the charged cur- 
rent reaction: 

e 

but also the neutral current reaction .which can be produced by 
any type of neutrino and therefore can be used as a flux nor- 
malization reaction: 



v + d~*n+n+v 



216 - 



where v stands for an arbitrary mixture of neutrino types. 
Table III shows their results. 

TABLE III 
Data summary for V -* D reactor experiment Ll7j 



Reaction 


Reactor on 
events /day 


Reactor off 
events/day 


Net rate 
reactor associated 


V +D — n + n +V 

X X 

V +D -* n +p + e~ 


425 ±2 
54 ±0.85 


351 ±3 
50.16 ±1.02 


74 ±4 
3.84 ± 1.33 



From the known detection efficiencies one can determine 
the ratio of observed cross -section s: 



ex p 



a(v + D —p + n + e + ) 



cr(v +D-n+ n+ v) 

v X x ' 



0.191 ±0.073 



which is independent of v-flux normalization, and of various 
instrumental biases and instabilities. The value of Ft can be 
predicted from the known cross-sections and after integration 
over v-fluxes one finds: 

R , =0.44 Avignone's spectrum [14] 



R th =0.42 Davis' spectrum [15] 



which is independent of the spectrum shape as anticipated and 
in substantial disagreement (about 3-3 standard deviations) from 
the experimental observa tions , thus reinforcing the speculation 
that neutrinos have performed significant oscillations from the 
reactor to the detector. Reines et al. [l6] have also compared 
these with previously published results and given the allowed 
region for mass difference and mixing angles (see Fig. 8). If 



- 217 



3.6 



3.2 



2.8 



^-^ 


2.4 


N 




> 




(O 




*"* 


2.C 


MM 




E 




I 


1.6 


<M — 




E 





1.2 



0.8 



0.4 - 



0.0 







ao a2 0.4 o.6 0.8 i.o 
Sin 2 20 

Fig. 8 

confirmed, these results will have fundamental importance in 
understanding the world of neutrinos. It must be noted that the 
existence of neutrino oscillations implies a neutrino mass. 
Since the number of neutrinos in the Universe is believed to 
be many orders of magnitude larger than for instance the nu- 
cleons, even a few electron volt of rest mass can significant- 
ly affect the total mass of the Universe. 



3. IS THE PROTON STABLE? 



3. 1 Present limit 

The best. limit up to day comes from the observation of 6 



- 218 



muons which stop and decay in the CWI [6] detector deep under- 
ground. The exposure was 67 tons x year and the muon detection 
efficiency about 0.5. In addition , some 600 counts over a thre- 
shold of 15-20 MeV have been recorded. The signal of muon de- 

3 

cays could be due to proton decay with tx . B of about 3x10 
years, where t is the proton lifetime and B is the branching 
ratio into muons or positive pions. Less stringent, but more 
general limits can be obtained from the single counts observed 
in the scintillators. 

A "reasonable" branching ratio B about 0.1 would then 

0! U 
2 9 2 9 

suggest t about 3x10 years or r > 10 years at a 90% confi- 
dence level. 



3.2 Current theoretical predictions 

A number of theoretical models [18] have predicted that 
protons should decay (see Table IV). Some of these models (es- 



TABLE IV 
Current Theoretical Predictions for Proton Decay 



<TB> years 


Lifetime Range 


Decay Modes 


Author and Model 


30 

5x 10 


io 30±2 


e +TT,Ci),p,T) 


Ellis, Gaillard, 
Nanopoulos (SU(5)) 


31 
10 


31±2 
10 


/J. decay 
suppressed 


Wilzek, SU(5), SO(10) 


32 
10 


- 




Georgi, Quinn , Weinberg 


31 
~ 10 


io 31±2 


e decays 


Goldmann > Ross , Marciano 
(su(5)) 


30 
«X 10 


_ 


MIT BAG 








Mode 2+e dec. 


Donoghue (SU(5)) 


- 


" 


Do not forget 
Muonic decays 


Weinberg, Glashow 


to 30 


io 2S ±io 32 


3V7T , vn 





- 219 - 

pecially the ones based on SO(5)) also give interesting predic- 
tions on the early stages of the big-bang process. Observation 
of this decay process would then at one hand explain the appa- 
rent excess of ordinary matter in the Universe as well contri- 
bute to the understanding of an overall unification of all 
forces (with exception of gravity). This very ambitious pro- 
gramme deserves consideration -and it has indeed spured a num- 
ber of new detectors to extend the sensitivity of the search 
for nucleon instability which are presently under construction . 

3.3 How to observe proton decay? 

t 3 3 

Let us assume we wish to reach a sensitivity of 10 years. 
Then in order to collect one event, we need to look at: 

10 years 3 

= 1.7 10 Tons x year 



2 3 

6x10 nucleons/ ton 



Assume a detection efficiency of 1/5 for the appropriate 
decay mode: we need to look at about 10 tons of target for one 
year in order to expect one possible decay event! Such a large 
mass and long time requires incredibly stringent conditions on 
background events. In particular the detector must be located 
sufficiently deep underground in order to remove as much as pos- 
sible cosmic ray associated backgrounds. The only irreducible 
background and eventually the ultimate limit will eventually 
be due to cosmic ray neutrino interactions .Various methods have 
been proposed and several detectors are under construction (see 
Table V). One can distinguish two distinct methods: 

1) Clear water calorimeters are the simplest and cheapest 
method which offers an acceptable spatial and time in formation ; 

2) A large scale electronic .detectors of the type used to 
study neutrinos at accelerator, made of sandwiches scintillators 
and of visual detectors (Conversi tubes). 



- 220 - 



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It is too early to say which one of the two approaches 
would eventually lead to success. Unless these 'detectors are 
buried very deep underground the muons traversing the detector 
and their secondaries must be rejected to an incredible level. 

3.4 Planned ultra large mass proton decay detectors 

A super massive detector (> 10 Tons) is being discussed 
[19] . For these fiducial masses, only clear water is conceiv- 
able. W. Huffmann [19], has proposed a new light multiplying 
device in which photocathode surface in excess of one square 
metre can be obtained with a cylindrical multiplying phototube 
of about 30 cm diameter and about 3 metre long. 

3.5 By-product of proton decay experiments 

3 4 

Large (10 -10 Tons) detectors underground would observe 
also in excess of 10 neutrino events produced within the fi- 
ducial volume. Events of type v , v will be identi fied. A good 
calorimetric energy resolution is expected ( ±10% at about 1 GeV) . 
Finally the determination of the energy flow can be used to 
determine the direction of the incoming neutrino with an un- 
certainty of about Ap =±150 MeV/c. This will provide a good 
measurement of low energy neutrinos across the earth's diameter 

— 3 

and be sensitive to neutrino oscillation down to A/» = 10 eV. 
Furthermore it could detect extra terrestrial neutrinos from 
point sources, like for instance stellar collapses. Clearly 
these experiments are very interesting and can provide us with 
information complementary to that available from acceler- 
ator experiments. 



222 



REFERENCES 



[l] PONTECORVO B. : n JETP Sov.Fix." 53 (1967) 1117; BEREZINSKI S.M. and 
PONTECORVO B. : "Proceedings of the Baksan 1977, Conference on Neutrino 
Physic and Astrophysics" pag.267, Vol.11. 

[2] BEREZINSKY V.S. and PRILUTSKY 0. F. : "Proc. of 1976 Int. Aachen Conf. 
on Neutrino Physic" H. Faissner Ed., pag. 650. 

[3] STEIGMAN G. , private communication during an excellent dinner in Tra- 
stevere (22 February 1980). 

[4] ACHAR C. V., MENON M.G.K., NARASIMHAN V.S., RAMANA MURTHY P.V. , SREE- 
KANTAN B.V. , HIMOTANI K. , MIYAKE S. , CREED D.R., OSBORNE J.L., PATTI- 
SON J.B.M., WOLFENDALE A.W.: "Phys . Lett . "iS, 196(1965); KRISHNASWAMY 
M.R. , MENON M.G.K., NARASIMHAN V. S. , HIMOTANI K. , ITO N., MIYAKE S. , 
OSBORNE J.L., PARSONS A.J., WOLFENDALE A.W. : "Proc Roy. Soc. London" 
A 323, 489 (1971). 

[5] REINES F. , KROPP W. R. , SOBEL H. W. , GURR H.S. , LATHROP J.F. , CROUCH M. F. , 
SELLSCHOP J.P.F., MEYER B. S. : "Phys. Rev." D4 , 80 (1971). 

[6] CROUCH M.F. , LANDECKER P. B. , LATHROP J.F. , REINES F. , SANDIE M.G. , 
SOBEL H.W., COXELL H. , SELLSCHOP J . P. F, : "Phys .Rev. "D18, 2239 (1978). 

[7] CHUDAKOV A.E., MAKDEV B. A. , MALOVICKO Yu.V., MARKOV V.Yu., MIKHEYEV 
S.P. , STEPANOV V.I., ZAKIDYSHEV V.N.: "Proceedings of the XVIth Con- 
ference on Cosmic Rays-Kyoto 1979" Volume MN 5-6., pag. 287. 

[8] Private communication of CHUDAKOV A.E. to Cline'D. 

[9] WOLFENSTEIN L. in "Proceedings of 1978 Purdue Neutrino Conference". 

[lO] BELLOTTI E. et al.: "Letters Nuovo Cimento" 553, 17 (1976); BLIETSHAN 
J. et al.: "Nucl . Phys . " B133 , 205 (1978). 

[ll] CNOPS AM. et al.: "Phys. Rev. Lett." U0 , 144 (1978). 

[l2] WACHSMUTH H., CERN-EP/79-1 15 , .1979, to appear in the "Proc. of the In- 
ternational Symposium on Lepton and Photon Interactions at High En- 
ergies, FNAL, Batavia, Illinois ,' 1979" ; and see also DE RUJULA A.,. 
LUSIGNOLI M. , MAIANI L. , PETCOV S.T. , PETRONZIO R. , CERN preprint TH - 
2788, 1979, to appear in "Nucl. Phys. B. n . 

[l3] REINES F. in "Unification of Elementary Forces and Gauge Theories", 
Edited by D.B. Cline and F.E. Mills (Harwood, London, 1978), p. 103. 

[14] DAVIS B.R. , VOGEL P., MANN F.M. and SCHENTER R. E. : "Phys. Rev." D19 , 
2259 (1979). 

[l5] AVIGNONE III F. T. and GREENWOOD Z. D. (University of South Carolina, 
preprint Feb. 1979). 

[l6] BARGER V., WHISNANT K. , CLINE D. . PHYLLI PS R. J. N. , COO-881-135 Univer- 
sity of Wisconsin preprint, Feb. 1980, submitted to "Physics Letters". 



- 223 - 

[l7] PASIERB E., GURR H.S. , LATHROP J., REINES F. and SOBEL H.W.: "Phys. 
Rev. Lett." k3 , 96 (1979); REINES F. , SOBEL W.H. and PASIERS E. , Evi- 
dence for Neutrino Ins tabi I i ty , University of California, Irvine, to 
be published in "Phys. Rev. Lett." April 1980. 

[18] PATI. J.C. . SALAM A.: "Phys .Rev. Lett . " 31,661 (1973); "Phys .Re v. " Dl 0, 
275 (1974); 

GEORGI H. and GLASHOW S.L. : "Phys .Rev . Lett . " 32, 438 (1974); 
GEORGI H. , QUINN H.R. , WEINBERG S. : "Phys. Rev. Lett." 33, 451 (1974); 
GEORGI H. and NANOPOULOS D.V.: '"Phys. Lett." 89B, 392 (1979); BURAS 
A.J., ELLIS J., GAILLARD M.K., NANOPOULOS D. V. : "Nucl.Phys." B135 , 66 
(1978); ROSS D. : "Nucl.Phys." BUO, 1 (1978); 
JARLSKOG C. and YUDURAIN F.J.: "Nucl.Phys." B149, 29 (1979); 
MACHACEK M. , Proc. of the XIV Rencontre de Moriond, J.Tran Thanh Van, 
Ed., 1979. GOLDMAN T.J. and ROSS D.A. , Caltech 68-704 (March 1979). 

[19] HUFFMANN W. , RUBBIA C. and WINN D. , paper presented at the 1980 Vienna 
Instrumentation Conference, April 1980. 



225 



RICCARDO GIACCONI ( * } 



X-RAY ASTRONOMY - RECENT RESULTS 



Observation of astronomical objects in the X-ray range of 
wavelengths has progressed rapidly in the last two decades , fi rst 
with rocket (Giacconi et al., 196-2) and later with satellite- 
borne instrumentation. The use of increasingly larger and so- 
phisticated orbiting observatories utilizing non- focusing in- 
struments , which started with UHURU in 1970 (Giacconi et al., 
1971) and culminated with HEAO-1 in 1977, has permitted the 
study of the most luminous galactic sources such as pulsars, 
supernova remnants, binary X-ray sources and bursters in the 

35 39 — 2 — 3. 

range of luminosities 10 -10 erg cm sec in the 1-10 keV 

range. In extragalactic ast ronomy the closes t and/or most power- 
ful of the extragalactic sources could also be detected. Some 

- 7 - 2 - 1 

500 sources ranging in fluxes 5 at Earth from 10' erg cm sec 

-11 -2-1' 

to 10 ergcm sec (1-10 keV) have been catalogued. 

The recent launch of the Einstein Observa to ry (Giacconi et 
al . ,1979a), which introduces the- use of focusing optics to ex- 
trasolar X-ray astronomy, has resulted in a thousand-fold in- 
crease in sensitivity (S . ^10 ere cm sec in the 1-3 keV 

•'Bin ° 

range), coupled with the achievement of imaging capabilities 
over fields of approximately 1/3 with angular resolution of 
approximately 3 arc seconds. 

This qualitative change in observational capabilities has 
so broadened the scope of X-ray observations that it now en- 
compasses essentially all objects studied in Astronomy from the 
planet Jupiter to the most distant known clusters and quasars. 

The detection of X-ray emission from stars throughout the 



(*) Harvard-Smithsonian Center for Astrophysics, Cambridge, Mass. U.S.A. 



- 226 



HR diagram (Vaiana et al.,1980) at levels orders of magnitude 
greater than predicted by current theories of corona formation 
and heating, promises to revolutionize our understaading of the 
role of rotation and magnetic fields in the turbulent transport 
of energy from the core to the exterior layers of a star. The 
reformulation of the theory which is forced by the observation 
will have significant consequences on models for stellar for- 
mation and evolution. 

The detection of individual high luminosity X-ray sources 
in nearby galaxies promises a new insight into the question of 
stellar content of galaxies and its dependence on the chemical 
composition and evolutionary state of the parent galaxy (Van 
Speybroeck et a 1 . , 1979 ; Long et al.,1979). 

The study of active galactic nuclei has made great strides 
with the first detection in X-ray of jets in 3C273 (Henry et 
al.,1980), M87 (Schreier et al.,1980) and Cen A (Feigelson et 
al.,1980) and with the extension of X-ray observations to sta- 
tistically meaningful samples of emission line galaxies, Sey- 
ferts , BL Lac objects and QSO' s up to Z=3.5. The question of 
evolution of active galaxies in general and QSO' s in particu lar 
is intimately related to the question of the origin of the iso- 
tropic X-ray background (Giacconi et al . , 1979b; Murray et.al., 
1980). 

The observation of X- ray emission from clusters of galaxies 
(Forman et al.,1979; Jones et al . , 1 979) ,has revealed a complex 
morphology which seems to be intimately connected to the state 
of evolution of the Clusters. Investigations on mass distribu- 
tion, state of relaxation, origin of the gas and the effect of 
the cluster environment, on the component galaxies are now in 
progress. X-ray observations of the most distant known clusters- 
have been used to confront theories of cluster evolution (Henry 
et al. , 1979). When extended to' even more distant: clusters, 
they will play- a unique role in the study of the= early stages* 
of cluster- formation. ■,;,■■•'■ 

Siace it is clearly impossible to encompass all these to- 



- 227 



pics, I have selected among them those that seemed to me more 
clearly relevant to the subject of this symposium. First, I will 
deal with recent advances in the study of compact objects which 
is relevant to questions of the behavior of matter at extremely 
high density. In the latter part of this paper, I will address 
those recent advances which are relevant to cosmological stud- 
ies and, in particular, the subject of cluster investigations 
and the closely related subjects of X-ray emission of QSOs and 
their X-ray background. 



COMPACT GALACTIC X-RAY SOURCES 

The discovery of pulsars (by radio techniques) and of bi- 
nary X-ray sources and bursters (through X-ray observations) 
permit us to investigate the structure and properties of neu- 
tron stars. The relation between the observable quantities and 
such fundamental parameters of the neutron star as magnetic 
fields, structure and dynamics, surface temperatures, radii, 
mass and equation of state have been discussed extensively in 
the literature and most recently summarized by Pines (1980), and 
I will not discuss them here in detail. I will briefly summar- 
ize some of the by now classical observational results pre- 
Einstein, and then discuss recent observations with Einstein 
which are relevant to this research. 

Since the early suggestion by Baade and Zwicky (1934) that 
supernovae explosions would result from the collapse of a normal 
star to a neutron star "consisting of extremely closely packed 
neutrons", a number of theoretical astrophysicists considered 
the possible existence of such stars culminating in 1939 with 
the computation of an upper limit on its mass of 0.7 M & by Op- 
penheimer and Volkoff ( 1939) .Not unti 1 the late seventi es , fol- 
lowing the work of Burbidge, Burb'idge, Fowler and Hoyle (1957) 
on nucleosynthesis could more realistic models of star pre-su- 
pernova explosions be computed. These authors studied the pos- 



228 



sible transformation of an iron core to Helium. Soon thereafter 
Cameron suggested the possible collapse of an iron core to a 
neutron core through inverse beta decay (Cameron , 1958) . Cameron 
and his collaborators (Cameron, 1959) as well as other authors 
(Harrison et al.,1958; Ambarzumian and Saakyan, 1971) computed 
models for neutron stars with a detailed treatment of surface 
layers and a discussion of the possible equations of state and 
the possible ranges of M, R and p. 

These studies received new impetus after the discovery of 
Sco X-l (Giacconi et al . , 1962). On the basis of core temperature 
computations by Chiu (1964) and of surface temperatures by Mor- 
ton (1964), it appeared possible that Sco X-l, as well as the 
X-ray source in the Crab Nebula, could be a neutron star emit- 
ting X-ray radiation by thermal processes. The discouraging re- 
sults of the Friedman 1963 Crab occultation experimen t (Bowyer, 
1964) , which failed to detect the Crab pulsar, left open the 
question of the possible existence of neutron stars which was 
settled on ly by the ' discovery of pulsars (Hewish, 1967) and by 
their subsequent interpretation as a magnetized spinning neu- 
tron star. Given observational evidence for the existence of 
neutron stars, new impetus was given to theoretical investiga- 
tions. Observational work in the X-ray domain was also progress- 
ing at a rapid rate. Pulsations were observed from NP 0532 in 
X-rays (Fritz et al.,1971), which revealed that young pulsars 

2 5 

emit most of their energy in the X-ray domain (L^IO L ^-10 L R ) . 
The UHURU di sco very of close mass exchange binaries (Giac- 
coni et al.,1971; Tananbaum et al . , 1 972 ) containing a collapsed 
object (neutron star or black hole) opened the possibility of 
studying neutron stars in a new astrophy sical setting. X-ray 
measurement of the Doppler shift of the period in regular ly - pul- 
sating sources, combined with radial velocity measurements of 
the companion star, yielded the first independent measurement 
of neutron stars. The best current estimates range between 1..3 
and 3.0 Mq, -the large uncertainty in individual measurement 
being mainly due to the diff icu lty of obtaining precise optical 



- 229 



determinations of radial velocity in a system bathed in X-rays 

(Fig. 1) . The relation between the spin up rate P and the quan- 

3/7 
tity PL , has been determined for a number of the X-ray objects 

(Ghosh and Lamb, 1979). 



T 



I 



I 



I 



1 



1 



4 4U0900-40 



SMC X-l 



Cen X-3 



Her X-l 



PSR 1913+16 



h 4UI538-52 



J L 



12 3 4 

Neutron- Stor Moss (Mq) 



Fig. 



and found to be in good agreement with that which can be com- 
puted for disk accreting sources , assuming a particular stellar 
magnetic moment of 4.8*10 gauss cm ,a particular equation of 
state (Pandharipande, Pines and Smith, 1976)\and range of mas- 
ses (Figure 2). The results are weakly dependent on the last 
two parameters (Ghosh and Lamb, 1978). It should be noted that 

if the accreting object was assumed to be a white dwarf, the 

3/7 
predicted locus of points in the P PL diagram would be shif- 

ted by two orders of magnitude. 

Pines and his collaborators emphasized the power of X-ray 
timing observations to determine magnetic moments, as described 
above, and cru-st core -coupling as can be achieved by angular 



230 




Fig. 2 



velocity fluctuation analysis (Lamb, Pines , Shah am, 1978). Boyn - 
ton and Deeter (1979) carried out such an analysis for Her X-l, 
by constructing the power spectrum of torque fluctuations using 
UHURU observations. They found no structure in the power spec- 
trum which implies constraints of the crust-core coupling time 
of 1 < 7" c < 100 days and/or relative equality between crust and 
core moments of inertia. 

Pines and his co-workers have emphasized the extent to 
which our lack of knowledge of the basic interaction between 
neutrons results in significantly different neutron star con- 
figurations depending on the assumed potential for neutron - 
neutron interaction. This is i llus tra ted »in Figures 3 a and b 
where the neutron star mass is given as a function of central 
density for soft (Reid potential.) and hard (TI interaction) 
equations of state. The Reid potential corresponds to models 



231 - 




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- 232 




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- 233 - 

for which the average system interaction energy is attractive 
at nuclear density and the TI interaction model corresponds to 
models for which the average system interaction energy is re- 
pulsive at subnuclear density ( Pines, 1980 ). Two quite di fferent 
models of neutron stars emerge between which, however, timing 
measurements have not yet been able to discriminate, Figure 4. 
A different, and perhaps more promising approach to the 
study of this problem can , however, be undertaken using Einstein 
observations. A great deal of theo retical computations have been 
carried out following the early work of Bahcall and Wolf (1965) 
on the cooling of neutron star co res .Tsuru ta (1974) and Malone 
(1974) established the relation between core and surface tem- 

- 2 

perature (Ts/Tc X10 ) and, stimulated by newly obtained tem- 
perature limits for black body X-ray emission from pulsars 
(Wolff et al.,1975; Toor and Seward, 1977 ), Tsuruta and Maxwell 
developed cooling laws and carried out detailed computations 



COOLING CURVES 

(C) IV) 



M-1.3M 
H-5>10 ,2 G 




3 4 5 

LOG TIME (years) 



Fig. 5 



234 



of Ts vs t. They showed that the cooling depends on magnetic 
fields, superfluidity , solidification of the outer layers, stel- 
lar masses, but most of all on the specific model adopted for 
nuclear interactions which determines the equation of state and 
the presence or absence of pion condensates (Tsuru ta, 1979) , Fi - 
gu re 5 . 

The Einstein observatory permits us to refine the measure- 
ment (or upper limits) of the temperature of neutron stars and 
thus confront these theories with observations. The study of 
historic supernovas permits us to search for black-body radia- 
tion from neutron stars of known age; the search for black-body 
emission from pulsars gives us temperature limits for neutron 
stars of unknown age, but for which the absence of a supernova 
remnant allows more sensitive detections. 

In a qualitative way our finding can be summarized as fol- 
lows: no point source is found at the center of any historic su- 
pernova remnant except for Crab and Vela. This is shown, for ex- 
ample, in Plate I a-b where an X-ray image of Cas A and Tycho 
obtained with the high resolution detector on Einstein is shown. 
Mean velocity of radio pulsars from proper motion measurements 
is known to be about 150 km s" , wi th maximum known velocities of 
500 kms~ . In the few hundred years since the explosion , neu tron 
star remnants with these velocities could not have moved more 
than 10 to 20 arc seconds from the center. An upper limit on the. 
temperature of a black-body source that could escape detection 
is 1.5*10 e °K (Murray et al., 1979) for Cas A and 1 . 8 * 10° °K 
(Helfand et al.,1979) for Tycho. Quantitatively the results for 
historic remnants are summarized in Table 1, where upper limits 
are shown for most supernova remnants, - the only two positive 
detections being Crab and Vela. 

The measurement for Crab is the result of a long exposure 
image of Crab with timing information preserved for each incom- 
ing photon. The time integrated image is shown in Plate II a. 
We have folded the data modulo a constant period in the frame 
of reference of the solar system center of mass. For the total 



235 - 











TABLE 


1 


Name 




Age 

(yr) 


D 
(kpc) 


Kax* 
(') 


T 

(10 e K) 


Cas A 




^300 


2.8 


0.4 


< 1.5 


Kepler 




3 75 


8.0 


0.2 


< 2.1 


Tycho 




40 7 


3.0 


0.5 


< 1.8 


Crab 




925 


2.0 


1.6 


< 2.5 


SN1006 




9 73 


1.0 


3.3 


< 1.0 


RCW86 




1794 


2.5 


2.5 


< 1.5 


(AD185) 












W2 8 




3400 


2.3 


5.0 


< 1.5 


G350.0- 


18 


4 
~i0 


4.0 


7.0 


< 1.5 


G22 .7-0 


2 


4 

~i0 


4.8 


7.0 


< 1.8 


Vela 




4 

^10 


0.4 


1.4° 


< 1.5 



Reference 

Murray et al. , 1979 
Helfand et al., 1979 
Helfand et al. , 1979 
Harnden et al. , 1980 
Pye et al. , 1980 
Helfand et al. , 1979 

Helfand et al. , 1979 

Helfand et al. , 1979 

Helfand et al. , 1979 

Harnden et al. , 1979 



Distance from SNR center assuming a transverse velocity of 1000 km s 



image and for the point source we find the results shown in the 
two histograms in Figure 6. We can determine the steady unpulsed 
emission of the point source by subtracting the contribution 
of the nebula from the emission of the point source. The re- 
sidual at the minimum of phase is clearly evident. This effect 
can be seen also by examining the images at different phases 
as shown in Plate II 6. The effect can be due ei ther to residual 
pulsar radiation or to black-body emission. In Figure 7 the spec- 
trum of the nebula and pulsar over the range from radio to X- 
rays is shown. It is worth noting that a steady component of 
approximately 3% of the maximum pulse is observed in the visible 
wavelengths as well (Peterson, et al., 1978). This clearly can- 
not come from a continuation of a black -body spectrum at 2.5 10 K 
which we obtain by assuming a distance of 2 Kpc and a neutron 



- 236 




s±Nnoo 



237 



-22 


_ 


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1 ' 1 ' 1 ' — 1 


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Log frequency, Hz 


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Fig. 7 

star radius of 11.1 km (stiff equation of state) and is quite 
possibly due to pulsar radiation. This raises the possibility 
that the X-ray emission we observe is also due to pulsar emis- 
sion and not black body. We hope in the near future to use a 
filter technique to distinguish between a power law and black- 
body contribution. Very similar considerations also, apply to 
the study of the Vela pulsar (Ha rnden, 1 979) ; in this case, how- 
ever, no X-ray pulsations are found and the temperature of the 
black body is obtained by assuming that all the radiation we 
see from the neutron star is due to thermal emission. 

These data have been compared by Tsuruta (1979) with the 
predicted cooling curves under a number of assumptions, Fi gure 5. 
Current values appear to be at the limit allowed by her compu- 
tation for stiff equations of state (no pion cooling). However, 
Lamb and his co-workers have recently pointed out that in the 
case of a neutron star, not only the equation of state but also 
energy transport processes must be treated in the fully rela- 



- 238 



tivistic approach to give realistic estimates. Preliminary re- 
sults of these computations show that the temperatures can be 
lower by a factor of 2 than those previously calculated for any 
given models. Thus, in their opinion, no definite conclusion 
can yet be reached on the presence or absence of pion conden- 
sates. 

In the case of radio pulsars an extensive search with the 
Einstein Observatory for X-ray emission has resulted in a large 
number of upper limits on the temperature summarized in Table 2 
(Helfand et al.,1979) and one possible r.ecent detection by the 
Columbia group using Einstein data, that of PSR 1055-52 at an 
equivalent black-body temperature of approximately 10 °K. Pos- 
sibly this is related to the fact that PSR 1055-52 is one of 
the younger pulsars since its period is of 0.119 seconds. Ob - 
servationally the sensitivity for detection of such isolated 
objects is finer than can be reached for objects embedded in a 
nebula. However, the comparison of the data with theory is ham- 
pered by the lack of knowledge of the age and by the possible 
increasing importance of heating mechanisms such as frictional 
heating (Greenstein, 1975), or polar cap heating (Ruderman and 
Sutherland, 1975). It is clear that much observational and 
theoretical work needs to be done to clarify this picture. The 
potential returns are, however, very exciting since the study 
of neutron stars internal structure may give us information on 
such fundamental problems in. physics as the basic interac- 
tion between Hadrons. 

Much more could be added on the impact of X-ray astronomy 
observations on the study 'of collapsed stars. In particular, X- 
rays offer a unique tool for the identification of black holes. 
Cyg X-l, the erratically flickering X-ray source, is still the 

— 3 

most promising candidate. It is compact (about 10 light .sec- 
onds) and massi ve (> 6 Mq) and the possibility that we may be 
fooled on these conclusions by the presence of a third body in 
the systems seems less and less tenable. On the other hand, 



239 - 





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- 240 - 

theoretical limits on the mass of neutron stars for a great 
variety of equations of state seem to converge to about 2 solar 
masses andupper limits of 3 and 5 solar masses have been obtained 
by Rhoades and Ruffi'ni (1974) and by Hartle '( 1978) respectively . The 
definite confirmation of this discovery would have great, sig- 
nificance • for physical theory as a verification of the theory 
of general relativity in a completely new regime. Not much pro- 
gress has occurred in the last few years in the field due pos- 
sibly to lack of observational opportunities. 

TTie Einstein Observatory is not particularly suited to study 
fast time variability since its sensitivity derives not from 



GLOBULAR CLUSTER X-RAY SOURCE POSITIONS 
RELATIVE TO CLUSTER CENTER 
(NORMALIZED TO CORE RADIUS) 




Fig. 8 



- 241 - 

large collecting area (only about 300 cm ),but by the improve- 
ment in signal to noise. The most substantial contribution of 
recent Einstein observations in this field has been a negative 
one, with the determination of the probable mass range of the 
bursting X-ray source in the globular clusters. 

Although the consensus seems to have favored in the last 
few years models of burst sources, based on low mass binaries 
(about 2Mq) containing a neutron star (see e.g. Joss, 1979) 
rather than to those based on spherical accretion on massive black 
holes (>10Mq) still no definitive proof of the binary nature 
of burst sources has yet been found. 

The high angular resolution capabilities of Einstein have 
been brought to bear on the problem. The X-ray position of 8 
X-ray bursters has been measured with respect to the center of 
the globular clusters in which they are contained. It has been 
shown theoretically that the spatial distribution of these ob- 
jects within the core yields on a statistical basis a measure 
of the mass (Bahcall and Wolfe, 1976). The results are shown in 
Figure 8. A preliminary analysis indicates that the most prob- 
able mass of the X-fay emitting system is of order 2 Mq thereby 
making it less likely, although not completely excluding that 
these sources may be massive (> 10 M Q ) black holes (Grindlay, 
1980). 



EXTRAGALACTIC X-RAY SOURCES 

I would like to turn now briefly to completely different 
topics in X-ray astronomy which are beginning to be relevant to 
cosmological studies and which we can safely predict will be- 
come even more important in the next few years. 

The first topic is the study of high temperature inter- 
cluster gas. This component of clusters, which was first re- 
vealed by UHURU X-ray observations, gives us a unique tool to 
study the properties of clusters as a whole, as well as the in- 



- 242 



teraction of individual galaxies with the medium. 

Preliminary results from Einstein Observatory (Jones et 
al., 1979) reveal a complex morphology which is illustrated in 
Plate III a-b where two extreme examples of cluster gas con- 
figurations are shown. Such features have been related to cluster 
properties and evolutionary state. Almost from the X-ray images 
alone clusters can be classified dynami cally .More quanti tati ve- 
ly centers and mass distributions can be obtained in X-rays with 
greater precision than at other f requenci es. Wi thout going into 
detail in the rich field of cluster phenomena, I would only like 
to mention some aspects of this study which have a bearing on 
cosmological problems. 



J7 



F v {4.8 x 10 Hz/U+2)) (erg cm' c s"' Hz"') 



.-2 .-" u,-i^ 




fv(2 keV/(l + 2»(keV cm" 2 $"' keV"') 



Fig. 9 



The first is the detection of the most distant known 
clusters at redshifts Z of about .8, which has been carried out 
by Henry (1979). Although as shown in Figure 9 the meager sta- 
tistical sample does not yet permit discrimination between dif- 
ferent evolutionary models.it is clear that X-ray observations 
give us a powerful tool for detection and study of clusters at 
very early stages of their formation. Even now the sensitivity 



243 - 



of Einstein is such that we could observe clusters at greater 
distances than any currently discovered in visible light, al- 
though observational time constraints will not permit an ex- 
tensive search for these objects. In the next generation of X- 
ray observatories, such observations will be extended to red- 
shifts of 2, with direct determination of redshi ft in the X-ray 
band, and to larger redshifts for simple detection . The consid- 
erable extension in redshi fts and therefore look-back time al- 
lowed by these measurements may help us to understand some of 
the very early stages of clusters' evolution from the density 
fluctuations of the early universe to the condensed state of 
here and now. 

Many authors have considered the use of cluster measure- 
ments for determination of cosmological constants. The inves- 
tigation of standard cosmologies reduces to the observational 
determination of the Hubble constant H and the deceleration 
parameter go, which together specify the density and size of 
the Universe; q > 1/2 for a closed Universe and q <l/2 for an 
open Universe. Measurement of g according to the classical test 
of galaxy magnitude versus redshifts has encountered difficul- 
ties because of selection effects and the lack of under standing 
of galaxy evolution .The test is unlikely to provide conclusive 
evidence for the case of a closed or open Universe, at least in 
the foreseeable future. 

A second classical test for qo is to measure the angular 
diameter of clusters as a function of redshift. Major uncer- 
tainties in applying this test, which include lack of knowledge 
about the evolution of the core radii of clusters and the mass 
distribution of the Universe also prevent this test from re- 
solving the question of the correct cosmologi cal model , although 
X-ray observations may improve this situation in the future. 

D. Schwartz (1976) has suggested a new test for go using 
cluster's of galaxies as the observational object. By using the 
theoretical relation for the differential number of objects at 
a given redshift instead of the relations for apparent magnitude 



- 244 



or apparent size, many of the difficulties encountered with the 
latter classical measurements of g , can be avoided. Homogeneity 
is required only on distance scales encompassing many clusters, 
at least tens of Mpc. Schwartz has proposed counting the num- 
ber of X-ray emitting clusters of galaxies per unit redshift as 
a function of redshift. At a Z of l,the ratio between the dif- 
ferential number curves for qo=0 and q =4 is about 4. The meager 
statistical sample available at the moment prevents this test 
from being carried out, but this deficiency should be remedied 
in the next few years. 

Recently Cavaliere (1978), Gunn (1978) , Murray and Boynton 
(1978), Silk and White (1978) havie proposed using X-ray and mi- 
crowave observations of the hot gas in rich clusters to give a 
direct and model-free measurement of the angular diameter dis- 
tance to clusters. The observations provide an evolution -in - 
dependent global method for the determination of both H and 
qo- In principle the determination could be carri ed out by using 
joint X-ray and microwave measurements of a few nearby rich 
clusters and a few clusters at Z¥l. The microwave observations 
are required in order to determine the diminution in intensity 
of the cosmic microwave background caused by Compton scattering 
on intervening hot cluster gas, as originally suggested by 
Sunyaev and Zeldovi ch , and to determine the microwave diminution 
core radius. The combination of the X-ray measurements of the 
cluster central temperature, the surface brightness, and the 
core radius with the microwave measurements of the diminution 
intensity and diminution core radius yields Hq independent of 
detailed modeling of the intracluster gas or of the cluster it- 
self. 

The actual application of these techniques is currently 
hampered by. the poor quality of the measurements, particularly 
in the microwave. Preliminary results of an analysis by Boynton 



and Murray, using Einstein results and a compilation of avail - 

-l-i 
able microwave data, yields for A2218 H o *50kms Mpc with an 

uncertainty of about ±40 (Boynton and Murray, 1980). 



245 - 



Finally, I would like to turn to the Einstein work on X-ray 
detection of QSO' s and the question of the X-ray background. 
While only the 3 nearest and/or most powerful QSO' s had been 
detected prior to Einstein, the increased sensitivity of the 
observatory now permits us to measure the X-ray flux from es- 
sentially all previously known quasars. Some 100 such objects 
have been observed ranging in-redshift up to the most distant 
known QSO' s at Z=3.5. More than 20 previously unknown QSO' s 
have been discovered in Einstein surveys and later identified 
through the optical work. The samples are not yet complete al- 
though quite substantial (e.g. 3/4 of 3 CR statistical sample). 

Tananbaum and his collaborators (Tananbaum, 1979) have 
studied the relation between optical and X-ray luminosity and 
have used an index a o which is the apparent spectral index be- 
tween 2500A and 2 keV. They find strong indications for changes 
in this index when comparing radio bright and radio quiet QSO' s 
and also when comparing nearby and distant (Z > 1 ) QSO' s (Table 
3). Since most QSO' s are radio quiet with Z>1, this means that 
the effective value of this index will be that appropriate for 
distant radio quiet objects <t o ^2il.5 (Henry, 1980). 

When this value is used in conjunction with optical number 
counts of QSO' s (e.g. Braccesi et al. ,1979) they find that the 
entire X-ray background could be given by their contribution 
if we extend the integral to objects of 21.5 magnitude. Henry 



TABLE 3 



« eff t 

(* for quasars 

ox ^ 





All Z 




Z < 1 


Z > 1 


Radio Loud 


+0.04 
l- 27 -0.03 


1 


+ 0.05 
• 25 -0. 04 


+ 0.0B 

l- 3 °:o.06 


Radio Quiet 


+ 0.05 
l- 44 -0.04 


1 


+0.08 
■ 34 -0.05 


+0.09 
1-58-0.06 


X-Ray Selected 


.. 


1 


.28±0.03 





- 246 



(1980) has also shown that the energy spectrum of the 27 bright- 
est QSO' s so far surveyed is consistent with an average power 
law energy spectral index of 0.4 as is found for the background 
in the 1-3 keV range. 

These findings are entirely consistent with the directly 
observed number of individual extragal acti c sources in the deep 
Einstein surveys (Giacconi et al., 1979b; Murray , 1980) which at 

-14 -2-1 

the limit of X-ray sensitivity (S . > 10 ere cm' s in the 

1-3 keV range) already produce an integral contribution equal 
to 25% of the background. When optical identifications are pos- 
sible, about 1/2 of the objects turn out to be QSO' s with 
0.5<Z< 2.6. 

These observations are relevant to cosmological research 
from several points of view. X-ray data furnish a powerful tool 
to select radio, faint QSO' s and they impose constraints on lu- 
minosity and/or density evolution of QSO' s in the past. These 
constraints are in agreement with recent findings from optical 
data of a turnover in luminosity evolution by Bahcall and So - 
neira (1980), by Kron (1980) and by Schmidt (1980). The fact 
that the major individual source contribution to the extra- 
galactic background is due to QSO' s of Z>1, and yet comprises 
to the limit of current X-ray surveys only 25% of the X-ray 
background, means that most of it must come from still larger 
redshifts. 

In the next several years sources with intrinsic luminosity 
comparable to QSO' s will be detectable by X-ray techniques to 
Z=5-10. X-ray observations may therefore make significant con- 
tributions to cosmological studies in the range of redshifts 
between the very small, whi ch are best studied in optical wave- 
length (Z'Zl), and the very large (Z^IOOO), which can be stud- 
ied in the microwave domain. 

This includes the bulk of the evolutionary history of the 
Universe and particularly .that epoch in which the formation of 
galaxies and clusters may have occurred. 



247 



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BAHCALL J. and WOLFE R. (1976) "Ap. J." 209, 214 

BAHCALL J. and WOLF R.A. (1965) "Ap. J." 142, 1254 

BAHCALL J.N. and SONEIRA R.M. (1980) preprint "Star Counts as an Indicator 
of Galactic and Quasar Evolution" 

BOYNTON P. and DEETER J. (1979) in "Compact Galactic X-ray Sources: Current 
Status and Future Prospects"; F.K. Lamb and D. Pines, Eds. (Physics 
Department, Univ. of Illinois, Urbana, 1979); p. 168 

BOYNTON P.E. and MURRAY S.S. (1980) preprint 

BOWYER S. , BYRAM E.T., CHUBB T. A., FRIEDMAN H. (1964) "SCIENCE" 146", No. 3646 
pp. 912-917, November 13 

BRACCESI A., ZITELLI V. , BONOLI F. and FORMIGGINI L. (1979) "Astr. Ap." sub- 
mitted for publication 

BURBIDGE E.M., BURBIDGE G. , FOWLER W.A. and HOYLE F. (1957) "Rev. Mod. Phys . " 

29, 547 

CAMERON A.G.W. (1958) "Mem. Soc. Roy. Sci. Liege" 5thSer.3, 163 

CAMERON A. G.W. (1959) "Astrophys. J." 130 , 884 

CAVALIERE A., DANESE L. and DE ZUTTI G. (1978); presented at XXI COSPAR 
Meeting, Symposium A. 

CHIU H.Y. and SALPETER E.E. (1964) "Phys. Rev. Letters" 12, 413 

FE I GEL SON E. (1980) contributed paper at the HEAD/AAS Cambridge, Mass. 
meeting 

FORMAN W. , SCHWARZ J., JONES C. , LILLER W. and FABIAN A.C. (1979) "Ap. J. 
(Letters)" 2J4, L27 

FRITZ G. , HENRY R. , MEEKINS J., CHUBB T.A., FRIEDMAN H. and HENRY R.C. (1971) 

"Astrophys. J. (Letters)" 16"4, L55 
GHOSH P. and LAMB F.K. (1978) "Ap J." 2 23 , L83 
GHOSH P. and LAMB F.K. (1979) "Ap J " 234, 296 

GIACCONI R. ,GURSKY H. .PAOLINI F.R. and ROSSI B.R. (1962) "Phys . Rev. Letters" 
9, 439 

GIACCONI R. .GURSKY H. , KELLOGG E.,SCHREIER E. and TANANBAUM H. (1971) "Ap. 
J. (Letters)" 167, L67 

GIACCONI R. .BRANDUARDI G. ,BRIEL U., EPSTEIN A. , FABRICANT D: , et al. (1979a) 
"Ap". J." 230, .540 

GIACCONI R. , BECHTOLD J. .BRANDUARDI G. , FORMAN W. , HENRY J.P.,et al. (1979b) 
"Ap. J. (Letters)" 234, LI 



248 



GREENSTEIN J. (1975) "Astrophys. J." 200, 281 

GRINDLAY J. (1980) talk at HEAD/AAS Cambridge, Mass. meeting, January 

GUNN J.E. (1978) Observational Cosmology, SAAS- FEE 

HARNDEN F.R. Jr. , HERTZ P. , GORENSTEIN P., GRINDLAY J., SCHREIER E. , SEWARD 
F. (1979) "Observations of the Vela Pulsar from the Einstein Observa- 
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HARRISON B.K. , WAKANO M. and WHEELER J. A. (1958) "La Structure et revolu- 
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HARTLE J.B. (1978) "Phys. Rep." 46, 201 

HELFANDD.J., CHANAN G.A. andNOVICK R. (197 9) preprint "Thermal X- ray Emis- 
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HENRY J. P. (1980) talk at the HEAD/AAS Cambridge, Mass. meeting, January 

HEWISH A., BELL S.J., PILKINGTON J.P.H. , SCOTT P. F. and COLLINS R.A. (1967) 

"NATURE" 217, 2 09 
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JOSS P.C. (1979) Comments on As trophy sics , in press 

KRON R.G. (1980) preprint "Colors as a Classification Discriminant 

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LONG K.S. and HELFAND D.J. (1979) "Ap. J. (Letters)" 2 34, L77 

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"Ap. J. (Letters)" 234, L69 

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January 
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2 76, 475 
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RHOADES CD. and RUFFINI R. (1974) "Phys. Rev. Letters" 32, 324 
RUDE-RMAN . II.Ai. and SUTHERLAND P.G. (1975) "Ap. J." 196, 51 



249 - 



SCHMIDT M. (1980). talk at the HEAD/AAS Cambridge, Mass. meeting, January 

SCHREIER E. (1980) contributed talk at the HEAD/AAS Cambridge, Mass. meet- 
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SCHWARTZ D.A. (1976) "Ap. J. (Letters)" 205, L95 

SILK J. and WHITE S.D.M. (1978) "Ap. J. (Letters)" 226, L106 

TANANBAUM H. , GURSKY H., KELLOGG E., LEVINSON R. , SCHREIER E. (1972) "Ap. 
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TANANBAUM H. , AVNI Y. , BRANDUARDI G. , ELVIS M. , FABBIANO G. , et al. (1979) 
"Ap. J. (Letters)" 234, L9 

TOOR A. and SEWARD F.D. (1977) "Astrophys. J." 216, 560 

TSURUTA S. (1974) Cooling of Dense Stars, in "Physics of Dense Matter"; D. 
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TSURUTA S. (1979) Thermal Properties and Detectability of Neutron Stars-I 
Cooling and Heating of Neutron Stars. "Physics Reports 56, 5; North- 
Holland Publishing Co. , Amsterdam 

VAIANA G. , et al. (1980) "The Einstein/CFA Stellar Survey", preprint 

VAN SPEYBROECK L., EPSTEIN A., FORMAN W. .GIACCONI R. , JONES C. etal. (1979) 
"Ap, J. (Letters)" 234, L45 

WOLFF R.S., KESTENBAUM H.L., KU W. and NOVICK R. (1975) "Ap . J. (Letters)" 
202, LI 5. 



- 251 - 

MILLA BALDO-CEOLIN ( * } 
SEARCH FOR NEUTRON-ANTINEUTRON OSCILLATIONS 



I will briefly discuss an experiment to be done at the 
nuclear reactor of the Laue-Langevin Institute in Grenoble [l] , 
which aims at detecting neutron Santineutron transitions with 
AB=2. 

The development of physics in the last years was aiming 
preferentially at finding unification and simpli city in the laws 
of nature. After the successful outcome of the unified theory 
of weak and electromagnetic processes, the grand unified theory 
including also strong interactions appears to open new very in- 
teresting possibilities. In fact a major consequence of that 
theory is that the baryonic number could be no more conserved. 

In the general framework of the grand unified theories S. 
Glashow [2] suggested that there could be an appropriate six- 
quarks-coupling leading to Afi=2 transition in nuclei, namely 
the process nN -* pions. According to this hypothesis, there must 
be a AB=2 neutron -antineutron mixing, characterized by a mass 
splitting 



Am =<n\H' \n> ~V r YAB=2)M (1) 

where T is the AB=2 decay rate and M is the nucleon mass. 

The interaction should be mediated by mesons, with the ap- 
propriate couplings and with a mass M intermediate between the 
grand unification and the weak -electromagnetic masses. 

An interesting consequence of this hypothesis is that an 
initially pur.e neutron beam becomes a neutron -antineutron mix- 



(*)"' Istituto di Fisica "G. Galilei" - Universita' di Padova - PADOVA 

Istituto Naz.ionale di Fisica Nucleare - Sezione di Padova - PADOVA. 



252 



ture after a finite time, the characteristic transition time for 
free neutrons being 

r t =-^- (2) 

n f Am 

Assuming that the stated limit on nucleon lifetime [3] 
also applies to this mode of decay, the derived limit for T n - 
i s 

r _ >i0 sec 
nn 

so that A m «iO" 21 eV & nd.M*>10° GeV. 

Rather than to look for a Afi = 2 decay process, which de- 
pends on Am squared, it seemed more appealing to search for a 
AB = 2 transition through a nz^n effect, which has only a first 
order dependence on Am. 

However, as we shall see, such an experiment is made dif- 
ficult for the fact that neutrons are never free in nature, and 
therefore their interaction with external electromagnetic or 
nuclear fields removes the degeneracy between neutron and an - 
tineutron states; this results in an energy splitting A£. 

The most general Hamiltonian describing a AB=2, CP con- 
serving, neutron -antineutron interaction is of the type 





H' 



where E is the free neutron energy. If a n^ii mixing exists, 
neutrons and antineutrons are no longer eigenstates: the new 
eigenstates are: 

ni = n cos 6 +n send ; n? = -n sen 8 +n cos 6 

n Am 
with tg 26 = — - . 

When a neutron beam is considered, the time development 



253 



- i£i t - iE 2 t 

factors for the new states nj. and n 2 are: e and e 



respectively, where 



?o +(&m Q 



Ei = E +( A m +AB 2 and E 2 = E Q - ( A m 2 +A£ 2 



The intensity of the antineutron component in a neutron 
beam after a propagation time t is given by 



.2 , \ i 

ir^O 'l(h.O) - sen 2 ( A m 2 +A£ 2 ) / 

A» 2 + AS 2 \ / 



A 2 / \M 

t (3) 

Am^+AS 1 



It appears that two situations are particularly signifi- 
cant: 

a) A£=0, i.e. free neutrons : the probability for a neutron to 

be found in an antineutron state is maximum, and P(n, t) =( — I , 
for (t.Sr); 

b) A£^0 and AE^Am: .PC?T, *) grows as t only for values of t very 
small such that Aff t < 1 {quasi free neutron condition). The 

/M 2 i 

maximum value for Pfn, t) is("7~ 1 .For t > — — , P(n,t) flue- 

/Amf VA£/ ** 

tuates between I — — I and 0. 
VAE/ 

It is worth noting that if AB>>Am the intensity of an - 

Am' 2 



tineutron component I(n,t) goes to zero as ( — — J -* 0, so tha.t 

n s± n transitions are suppressed and neutrons appear stable. 

In order to evaluate the effects of the external fields 
on neutron -antineutron transitions, we simply refer to the in- 
fluence of the magnetic field of the Earth. 

In this case, the energy splitting is ,AB = /jB = 10 eV; 

assuming Am-^10" eV, one has P(n, t) •£ 10 , a value which is 

• . i -4- 

reached after a time t <— — = 10 sec. Inorder that P builds up 

to a considerable value, it is imperative that the time t is as 
long as possible, which means A£ as small as possible. 



254 



Once the condition A£ t < 1 has been fulfilled, the sensi- 
tivity of an experiment which consists in detecting antineutrons 
in a quasi free neutron beam can be expressed in terms of <fi, T, 
t and 



r _ >s*[4JT t ; wh 



ere 



t is the neutron propagation time,0 is the neutron flux/second, 
and T is the duration of the observation. 

The experimental parameters determining the sensitivity 
are: 

i) the neutron flux: <fc; 
ii) the propagation length s and the neutron energy E, which 
determine the propagation time 

s 

t a — . 
Ye 

A rough -drawing of the experiment is given in Fig.l: cold 
neutrons from the reactor will be propagated in vacuum in a low 
magnetic field region. The beam will them be dumped on a Li 
target, and the possible antineutron component will be detected 
through the characteristic 2 GeV energy release of the anti - 
neu tron -nucleon annihilation processes. 

Neutrons come from a beam guide at the ILL reactor in Gre- 
noble. The energy of the transported neutrons, which have been 

- 3 

previously moderated in liquid deuterium, ranges from ^10 to 

— 5 9 

10 eV . The total flux is ~2'4 neutrons/sec. Fig. 2 shows the 
intensity and the divergence of the neutron beam as a function 
of their energy. The propagation then takes place along a vacuum 
pipe ~3 meter long, whose diameter varies from ^15 to ^65 cm 
in order to fully contain the aperture of the initial beam, thus 
preventing any interaction with the nuclei of the wall. Since 

- 2 - 1 

neutrons will take a time t = 10 +10 sec to run across the 3 
meter propagation pipe, the Earth magnetic field is correspond- 



- 255 




GO 

•H 

u. 



- 256 - 



, 9 

8 



10 



100 



wave length A [A] 
Neutron mean flux per unit wavelength per unit of solid angle 



10 



3 10 



10 









:::± ^£f- 




-j — ( 

S 1 




/ 1 

* t 


/_ 


" 1 

Ef44 ..j [ -I— -hi 1 1H 


::::::;£ : 


-1 

— 1 


/' 


1 


/ .. 





10 



100 



wave length [aJ 
Mean vertical — and horizontal divergency of the neutron beam. 

Fig. 2 

mgly reduced to B < 10' gauss by surrounding the pipe with a 
magnetic shield. 

After passing through this region of free propagation the 
neutron beam is absorbed on a Li target. The an ti neutron com- 



- 257 



ponent possibly present in the beam will then annihilate. 

A deposition of an energy 500 ^E < 1000 MeV in a total ab- 

3 

sorption detector ^100 x 60 x UO cm in size, in coincidence with 
a suitable signal from wire chambers just behind the Li tar- 
get, will represent the signal. 

Since .at the end of the pipe the neutron density will be 
^10 n/cm sec it is not expected that their interaction in the 
stopper can simulate the signal through a collective effect. 
Furthermore, the neutron beam is quite free from y contamina- 
tion since it is extracted through a curved guide. Mo reover since 
the intensity of the antineutron component is strongly dependent 
on the strength of the magnetic fi eld along the propagation path, 
a measurement carried out without the magnetic shielding will 
provide a direct check on the correct nature of the possible 
signals. 

To eliminate cosmic ray background the whole apparatus is 
shielded with iron and concrete and is covered with a set of 
counters in anticoincidence. 

In these conditions, in a 100 days running, r n _ will be 
measured up to 

r -=>fpF t = 3-10° sec 

Using realistic values for the neutron flux 4>, the propa- 
gation length s and the neutron energy E.,it appears reasonable 
to hope that the second phase of the experiment will be sensi- 
tive to oscillation times r - up to 10 +10 sec.; as an example 

nn 

for a propagation length s' four' times bigger than the present 

<P 3 4* 8 

one, and assuming — - = 2 • 10 — - one gets T nJi ^5'10 sec., cor- 
responding to a mean life for AB=2 transition in nuclei t~ n = 10 
years. 

Finally it may be interesting to compare the sensitivity 

for t — of this experiment with that which can be obtained in a 
■ ■ n n . 

search for AB=2 decay processes in nucl ear matter. An experiment 



- 258 



of the type of those designed to measure the proton lifetime 
(A6=i ) aiming at detecting AB=2 annihilation processes inside 
nuclei, requires, according to eq. (1), ^10 tons of material 



8 



in order to be sensitive to r _~5 # 10 sec. Such an enormously 



nn 



massive detector would also need a very high resolution to 
identify these events, which otherwise would merely constitute 
a background for the proton decay final states. 



REFERENCES 

[l] BALDO-CEOLIN M. , BATTY C.J., BYRNE J., FIDECARO G. , FIDECARO M. , GREEN 
K. , PENDLEBURY J.M., PUGLIERIN G. , SHARMAN P., SMITH K. : "A Search for 
Neutron-Antineutron Transition using free Neutrons Proposal at the 
ILL-HFR, 8-2-'80. 

[2] GLASHOW S.L.: "Proceedings of Neutrino '79" Bergen - Vol. I, pag.518. 
GLASHOW S.L. - This meeting. 

L3 J See for example: RUBBIA C. - This meeting. 



- 259 - 

FIFTH SESSION 
23 rd February 1980 - 9.30 a.m. 

Chairman: Edoard.oAm.aldi 



REMO RUFFINI ( * ) 



ON THE MAGNETOSPHERE OF COLLAPSED STARS 



ABSTRACT 

Much progress has been made in recent years on the know- 
ledge of gravi tationally collapsed objects thanks to a deeper 
understanding of relativistic field theories and to a large 
amount of experimental information obtained from x and gamma 
ray - radio and optical astronomy [l ] . Nevertheless, basic is- 
sues on the structure both of neutron stars and black holes re- 
main unanswered. 

Although in binaries x-ray sources neutron stars masses 
have been measured and they are in general agreement with the 
existing theoretical framework- [l] , we are still at large in 
the understanding of the basic features of the magnetospheres 
of neutron stars as well as on the details of their internal 
constitution. Still unanswered is the problem of how neutron 
stars transform their rotational energy in the observed elec- 
tromagnetic radiation of pulsars [2] .Possibly of relevance both 
to this issue and to the structure of neutron stars magneto- 
sphere 'are the gamma rays observations of Pulsars carried out 



(*) Istituto di Fisica "G. Marconi" - Universi ta' di Roma. 



- 260 - 

by the Cos B satellite [3] .The high level observed [3] in gamma 
ray emission both in the crab Pulsar (P3R0531+21) and in the 
Vela Pulsar (PSR0833-45) point to a highly efficient mechanism 
of transforming rotational energy into pulsed gamma radiation 
[2] . The characteristic double peak emission could be relevant 
in inferring the structure of the magnetic field near the neu- 
tron star surface [2] . 

In the study of the internal constitution of neutron stars 
a new tool of analysis comes from the x-ray observations made pos- 
sible by the Einstein observatory [4] and the theoretical work 
by Hong Yee Chiu and E. Salpeter [5], A. Finzi [6] and J. Bah - 
call and R. Wolf [7]. It is expected that the temperature of 
formation of a neutron star is !T~ 5 x 10 °k. The cooling of the 
neutron star will strongly depend on the presence of pions in 
the neutron star structu re. The upper limits established on the 
temperature of old pulsars [8] point to 'the possibility of di ffer- 
ent i at ing among neutron stars of different in ternal constitutions. 

The upper limits established on the temperature of the rem- 
nants of historical supernovae L9] , especially the one on Cas- 
siopea A [-9] point to the possibility of forming a fully gra- 
vitationally collapsed object (black hole) during the supernova 
explosion [l0] , [ll] . 

In the field of black holes much progress has been made 
both in the theoretical and experimental field. The macroscopic 
parameters characterising a black hole have been fixed [12] , 
Ll 3 J , [14] : the surface, the angular momentum, the rotational 
and Coulomb energy, the effective bulk viscosity, the electrical 
resistivity. Progress has also been made in the analysis of the 
perturbations and stability of a black hole [15] . In the ob- 
servational field two additional bynary systems presenting an- 
alogous features to Cygnus XI have been discovered [14] . 

The ast rophysi cal object presenting the greatest interest 
both from the point of view of supernovae evolution and the 
analysis of detailed relativis ti c effects i s the magnetosphere o f 
a gravi tationally collapsed star is SS433. This star discovered by 



- 261 



Stephenson and San du leak [l6j has been identified by Clark and 
Murdin [l7] to be correlated to a supernova remnant (W 50) ex- 
ploded approximately 30.000 years ago [l8].This source has also 
been found to be an x-ray source [19] . 

The very high redshi f ts {l+z = 1.17) and blue shift (i+z=0.c?9) 
observed in this source by Mammano et al . [20] and by Margon et 
al.[2l] can only be interpreted in terms of relativistic ef- 
fects. Models of this source have been proposed in terms of, 
(a) a very massive black hole [22], (6) a black hole of a few 
solar masses emitting collimated jets [23] and (c) of a rel- 
ativistic disc around a slowly rotating black hole [24] emit- 
ting the shifted lines by stimulated emission [25] . Selected 
aspects of these models wi 1 1 be discussed together with the pos- 
sibility of testing relativistic effects in the magneto sphere 
of the gravi tationally collapsed star. 



REFERENCES 

[l] See e.g. GIACCONI R. and HUFFINI R. : Ed. "Physics and Astrophysics of 
Neutron Stars and Black Holes" Noirth Holland - Amsterdam - 1978 - re- 
printed in 1980. 

[2] QADIR A., RUFFINI R. and VIOLINI L.: "Nuovo Cimento Lett." 27, 381 
(1980). 

[3] See e.g. D' AMICO N. and SCARSI L. : "The gamma ray sky at high energy. 
The role of Pulsars as gamma ray sources". "Proceedings of the first 
Austral Summer School" Ed. by C. Edwards - Springer - Verlag, Berlin 
1980. 

[4] See GIACCONI R. in these Proceedings. 

[5] CHIU H.Y. and SALPETER E.E. : "Phys .Rev . Lett ." 12, 413 (1969). 

[6] FINZI A.: "Phys. Rev. h 137B, 472, 1965, Ap. I. 139 , 1398 (1964). 

[7] BAHCALL J.N. and WOLF R. A. : "Phys. Rev." HOB, 1452 (1965). 

[8] HELFAND D.J. , CHANAN G.A. and NOVICK R. : "Nature" 283, 337 (1980). 

[9j SEWARD F. : personal communication. 

[lO] SHKLOVSKY I.S. : "Nature" 279, 703 (1980). 



- 262 - 

[ll] RUFFINI R.: Submitted to "Nuovo Cimento Lett.". 

[l2] RUFFINI R. : Ed. "Proceedings of the second M.Grossmann Meeting" -North 
Holland - Amsterdam 1980. 

[l3] DAMOUR T. : "Macroscopic properties of black holes" in ref. [l2] . 

[14] RUFFINI R. : "Gravitational ly collapsed objects" in ref. El2] . 

[15] FACKERELL E. : "Perturbation of Kerr -Neumann geometries" in ref . [l2] . 

[16] STEPHENSON C.B. and SANDULEAK N-: Ap. I. Supp. 33, 459 (1977). 

[l7] CLARK D.H. and MURDIN P.: "Nature" 276, 44 (1978). 

[l8] HOLDEN D.J. and CASWELL H.N., J.L.: "R.A.S." U3 , 407 (1969); 

GELDZAHLER B.J., PAULS T. , SALTER C.J.: "A. and A. Astronomy and As- 
trophysics" 1980. 

[l9] SEWARD F.D. , PAGE C. G. , TURNER M.J., POUND K.A.: "M.N. R.A.S." 175, 39 
(1976). 

[20] CIATTI F. , MAMMANO A. and VITTONE A.: IAU 3305, 1978; 

MAMMANO A., CIATTI F. , VITTONE A. : "As tronomy and As trophysics" (1980 ) . 

[2l] MARGON B. , FORD H.C. ,KATZ J. I. , KWITTER K. B. , ULRICH R. K. , STONE R.P.S., 
KLEMOLZ A.: "Ap. J. Lett." 230, L41 (1979); 

MARGON B. , FORD H.C, GRANDI S. A. and STONE R.P.: "Ap. J." 233, L63 
(1979); 

ABELL G.A. and MARGON B. : "Nature" 279, 7 01 (1979). 
[22] TERLEVICH J. and PRINGLE J.E. : "Nature" 178, 719 (1979); 

AMITHAl MITHCGRUB A., PIRAN T. , SHAHAM J.: "Nature" 279, 505 (1979). 
[23] FABIAN A.C. and REES M. : "Month. Not. R.A.S." 187, 13 (1979); 

MARTIN P.G. and REES M. : "Month. Not. R.A.S." 189 , 19 (1979)., 
[24] RUFFINI R.: "Nuovo Cimento Lett." 26, 239 (1979); 

FANG LI ZHI and RUFFINI R. : "Phys. Lett." 86B, 193 (1979); 

STELLA L. and RUFFINI R. : "Nuovo Cimento Lett." 27, 529 (1980). 

[2 5] STELLA L. and RUFFINI R. : "Phys. Lett." 91B, 723 (1980); 

ROSNER R. , RUFFINI R. and VAIANA G. : "On the recombination layer of 
the Dopplar SS433". 



- 263 



REMARK ON THE SPEECH OF PROF. R. RUFFINI 



CARAVEO.- I think a word of caution is needed about the 
"most important result in pulsar physics", as presented by R. 
Ruff ini, i. e. the fact that he -reported the detection of pulsed 
gamma radiation from five of them, namely Crab, Vela PSR 0740-28, 
PSR 1822-09 and PSR 1747-46. 

This is simply not so, yet. 

While the Crab and Vela pulsars are to be considered in- 
disputably as emi tters of pulsed gamma radiation , from the other 
three the level of confidence of the same process is by no means 
comparable. 

For 1747 the authors of the measurement (THOMPSON et al . 
1976, Astrophys .Lett . 17, 173) speak of a 4 ■ c single peak in the 
light curve, with a phase and shape (with respect to the radio) 
completely different from the Crab and Vela case. The other two 
pulsars have been mentioned as interesting candidate in some 
preliminary results by the COS -B satellite, but further obser- 
vations have so far failed to confirm these results. At this 
time, intense work is in progress by the COS-B Caravane Col- 
laboration to clarify this crucial matter. 

Meanwhile, it is not recommended to draw conclusions on 
the gamma-ray emission from pulsars based on more than the Crab 
and Vela cases, since the level of confidence of the various 
objects would be very inhomogeneous. 



- 265 - 

FRANCO PACINI (,) 
THE ACTIVITY OF GALACTIC NUCLEI 



The activity of galactic nuclei entails a continuous re- 
lease of energy in the form of hot gas, violent motions, rela- 
tivistic particles and ordered magnetic fields. The spectrum 
radiated spans most of the electromagnetic band, from radio - 
waves to y-rays, and the power can reach or exceed 10 -10 
ergs sec . Various extensive surveys dealing with this subject 
have been published recently (see , e. g. .Hazard and Mitton 1979; 
Physica Scripta 1978; Sett 1976;Wolfe 1979):we refer the reader 
to these publications for details. In the following we shall 
just outline the main ideas which are being discussed to ex- 
plain the origin of these phenomena which pose one of the most 
important problems of modern astronomy. 

1. In many sources one observes radio outbursts: the time^ 
scale t involved implies a size of the emitting region d£,cr 
(this does not hold for sources moving rel ati vis ti cally , Rees 
1967). Even before the advent of VLBI one had therefore learned 
that compact variable radiosources in nuclei of galaxies have 
a size ~i0 -10 cm. 

A standard compact source emits a spectrum which is op- 
tically thin at high frequencies and thick at low frequencies. 
In this case for v < v^ the usual synchrotron formulae apply. At 
lower frequencies the brightness temperature approaches the kin- 
etic temperature of the particles and the radiation is reab- 
sorbed. From the condition T. £'7V. we obtain 

o k in 



(*) Arcetri Astrophysical Observatory and University of Florence. 



■ \ A 



266 - 



2kv 2 ■ 2kv 2 n m c 2 

s < nr. . = fi— 

kln c 2 3k 

(fi is the solid angle subtended by the source, v =2 . 8 x 10 B 
Hertz is the gyro frequency) . 

The flux density S v cannot exceed a value which varies as 

2.5 

v ' and there must be a low-frequency cut-off at v = v . One 
finds that 

Sad 2 B' 1/2 v 2 ' S (optically. thick: v<v ) 

1-Ct -0C 

Sa/f B v (optically thin: v>v ) 

where is the angular diameter of the source. 

We note that the time at which the source becomes trans- 
parent depends upon the observing frequency because the source 
becomes optically thin at high frequencies first. 

This model has been fairly successful in explaining the 
observed variability of compact radiosources ,most notably that 
of 3 C 120. However in most sources the outbursts occur so ra- 
pidly that it becomes di f f icult to make a quantitative analysis 
of the evolution. Also, the above formulae assume a spherical 
geometry and nobody can assure us that this is what happens in 
galactic nuclei. 

The model of an uniform sphere which is instantaneously 
filled with relativistic electrons and magnetic fields, then 
expands at a constant velocity, is clearly unrealistic. In real 
life one must take into account the hydrodynamics of the ex- 
pansion, the finite acceleration times and the initial dimen- 
sions. 

Physical parameters in a compact source 

It is easy to see that the spectrum of a compact self- 
absorbed source yields important information concerning the 
internal physical parameters. Indeed in the optically thick 



- 267 - 



part 



kT. ~ mc 2 y 



Vi 



T b can bemeasured; y is given by the ratio I ] . One can there- 

fore measure the magnetic strength B which is connected with 
the gyrofrequency v g through the usual simple formula. In terms 
of observable parameters one finds ( for an electron energy dis- 
tribution N(E) aE' 2 ' S ) 




2 

B~2.3*10- S (-^) v \ 



(v m is GHz; 6 in milliarc seconds). 

Once the magnetic field has been determined, in the case 
of compact sources one can obtain the energy content in the form 
of relativistic electrons (and not just a minimum value as in 
the case of transparent sources). 

Calculations have been made by several authors for a var- 
iety of sources, the typical results are shown below: 



magnetic field B^10' 3±1 



gauss 



3 



brightness temperature T B ^10 1 °K 

volume emissivity ^ 1 milliWatt/ km 

energy content fj, ~ i0 62 - i0 50 ergs. 

The radioemitting volume could radiate high energy photons 
because of the inverse Compton process, and it is important to 
monitor the X-ray flux in order to find possible changes cor- 
related with the activity of the compact radiocomponen ts . 

2. The frequent; existence of variability in the optical 
and in the X-ray range with a much faster timescale (~hours) 



- 268 



suggests that most of the high frequency continuum comes from 
a smaller region, some 10 -10 cm across. This is not much 

8 

larger than the gravitational radius of a system with M ~ 10 Mo 
and indeed it is generally believed that active nuclei are pow- 
ered by the release of gravitational energy from collapsed ob- 
j ects. 

The models proposed invoke either the presence of a single 
massive body or a dense cluster of stars (normal or collapsed). 
The occurrence of outbursts involving much more than the energy 
released in the explosion of single stars argues in favor of 
massive objects. In addition, there seems to be a preferred 
orientation in the geometry and in the polarization properties 
of successive outbursts (see Wolfe 1979): again this suggests 
a coherent structure for the central engine. 

The mechanisms considered to release gravitational energy 
are either the infall of matter into a central object (accretion 
models) or the output of energy in the form of large scale elec- 
tromagnetic fields from the magnetosphere of rotating super- 
massive objects (electrodynamic outflow models) .Both mechanisms 
can work in principle and indeed -inside our own galaxy - they 
are responsible for the existence of compact X-ray sources and 
of pulsars. The main difference between them is that accretion 
is basically a thermal phenomenon whi le the presence of coherent 
electromagnetic fields naturally leads to the production of non - 
thermal particles. In real life, however, the difference is not 
always clear: for instance, in the case of accretion the pres- 
ence of magnetic fields embedded in the falling gas could lead 
to non-thermal aspects (acceleration of particles, flares...). 
Apert from that, it is still unclear whether the high frequency 
emission in galactic nuclei results from the presence of hot 
gases or whether it is genuine synchrotron and/or inverse Comp- 
tion radiation. In principle, the best possibility to distin- 
guish between accretion and electrodynamic outflow lies in the 
existence of the Eddington limit for spherical accretion: for 



26 9 



an object M ^ 10 -10 M this entails L ">- 10* S - 10*° ergs sec' * and 
an infall rate ~0.i-i M year' 1 (we assume an efficiency 10%). 
Although one may conceive accretion models which violate the 
Eddington limit by invoking special geometrical constraints, 
the evidence from compact X-ray sources in our own galaxy shows 
that in general this is not the case. The existence of many ex- 
tragalactic objects exceeding -the above limit would therefore 
represent evidence for electromagnetic outflow instead of ac- 
cretion (some examples already exist: 3C 273 reaches i0 47 ergs 
sec in the 7-ray range; NGC 1068 has a far infrared output in 
the range 10 -10 ' ergs sec' , etc.). Both types of models can 
be applied either to SM stars or to black holes. In the case 
of electrodynamic outflow the nature of the underlying obj ect 
is irrelevant: a black hole surrounded by a magnetized accretion 
disk behaves similarly to a classical magnetized supermassive 
object or spinar (Blandford and Znajek 1977). From an observa- 
tional point of view many recent claims for the discovery of 
black holes in galactic nuclei (such as M 87) are misleading: 
they just show the presence of a mass concentration in the nu- 
clear region, irrespective of whether the central obj ect is a 
black hole, a SM star or even a dense star cluster. Because of 
this reason, in the following we shall treat the central engine 
as a BLACK BOX rather than a black hole or a spinar and con- 
centrate on those aspects of the electrodynamic model which are 
independent from the particular nature of the central body. It 
is well known that in most cases thephysical parameters in the 
central region of active nuclei entail very fast radiative los- 
ses and require either a continuous reheating of the gas or -in 
the case of non-thermal processes - a continuous acceleration 
of particles. In the latter case this could be realized either 
by injecting new particles or by stirring continuously the same 
ones. The first scenario leads to. the expectation of a large 
number of "dead" parti cles which would depolarize the radiation 
because of the Faraday effect. This contradicts the observa- 
tions and one should therefore assume that the dominant pro- 



270 



cess involves re-acceleration in situ of pre-existing elec- 
trons. 

3. This requirement is naturally incorporated in the elec- 
trodynamic outflow models discussed by Pacini andSalvati (1978) 
(see also Cavaliere 1979). Basically, one assumes that in the 
central part of galactic nuclei the black box contains a spi- 
nar or a black hole surrounded by large scale electromagnetic 
fields where the acceleration and the radiation processes are 
equally fast. In other words, one cannot- distingu ish in a spa- 
tial sense between the electromagnetic field which accelerates 
and the one responsible for radiative losses: the particles are 
continuously accelerated in situ by the same fields (E^B) in 
which they are radiating . Thus they can reach a maximum Lorentz 
factor y such that the losses (cty ) inhibit the possibility 

of further gains. This point of view minimizes the overall en- 
ergy requirements for a given source and implies an energy out- 
put from the central body L equal to the total luminosity of 
the nucleus L... 

Due to the assumed nature of the braking torques on the 
spinar, the energy flux across the active region is of order 

L ~ B 2 cR 2 ~ I. 
e m 

For our purpose it is not necessary to know the details 
of the acceleration process as long as we can assume that the 
losses are sufficiently fast to establish equilibrium with the 
gains. If the Kl ein -Nishina limit allows Compton scattering up 
to the nth order, the total (synchrotron plus inverse Compton) 
luminosity of the active nucleus is given by 



L ~ L. 



.. \n/(n*l) 



'\B*cR's 



L a - (4/3)e<r T y u em N 



271 



(L s is the synchrotron luminosity; u. g is the energy density of 
the large-scale electromagnetic field; N is the total number 
of radiating particles). 

Under our assumptions L^L g which also holds for the Comp- 
ton luminosity L c ^L g . Indeed, in the simple homogeneous model 
the flux carried by the primary photons is of the same order as 
the flux carried by the field causing the synchrotron emission, 
and the respective energy densities are roughly equal: u^ u 
This causes a Compton output of the same order as the synchro- 
tron output. 

The frequency at which the available energy is radiated 
via the synchrotron process is 

eB 2 

v ~ y 

s 2-rrmc 

The previous equations completely determine the strength 
of the magnetic field in the active region, the number of ra- 
diating particles, and the characteristic Lorentz factor as 
functions of the following observable quantities: luminosity, 
spectral band where most of the synchrotron radiation is found, 
size of the active region (usually inferred from the time sca- 
le of variability). Once these quantities are determined, one 
can predict the properties of the resulting inverse Compton 
emission. If 

L R u 

£45 = — — — „ ; "is = — — ; ^13 



10^ ergs s' 1 10 iS cm lO™ Hz 



one finds 



B • ~ 1.8 x 10* L J'* K.d X (gauss), 
y-l.Jxio'^L^^R^' 2 



N ~ 2.(!M0 5 % 13 ; 1 I 45 1/2 fl 16 



272 - 



Most of the first-order inverse Compton emission should 
take place at a frequency 

v ~ 3. 7* lO 17 ^!? 2 £45 1/2 #15 Hertz 
c 



Wl 

men 



ith a luminosity L ~£ . We note that this is in good agree- 
t with the observational evidence for an X-ray luminosity of 
active nuclei roughly comparable to the IR-optical luminosity. 
As an example we can consider the nucleus of NGC 1275. 
Night-tonight variations in its optical continuum have been 
reported by various authors and imply an emitting region 
R£10 le cm with a total power L ~ 10 ergs sec' . Geller et.al. 
(1979) have recently discussed a model based upon the assump- 
tion that the IR-optical emission has a synchro tron origin while 
the compact X-ray source arises from inverse Compton scatter- 
ing. Standard considerations imply then a magnetic field strength 
8 ~ 10 gauss, y^lO -10 and a formal lifetime for the radia- 
ting particles ~ 10 sec. As noted by the authors, this requires 
a continuous re-acceleration process: the electrodynamic out- 
flow model takes care of this difficulty because the flux of 

2 2 

the Poynting vector B R c continuously replenishes the energy 
radiated away. 

4. The activity of galactic nuclei represents one of the 
main problems of modern astronomy. 

Some of the points presented earlier are rather strong, 
such as the fact that one is probably dealing with a single 
coherent engine rather than a multitude of them. Some other 
points (such as the question whether the object is a SM star 
or a black hole) are unsettled both from a theoretical and from 
an observational point of view. Black holes are supported by 
the astronomical fashion of the mid 70's and by the argument 
that they represent a likely outcome for the evolution of mas- 
sive stars and stellar systems. 



- 273 - 



REFERENCES 



BLAND FORD H. and ZNAJEK R. (1977), "M.N. R. A.S. " 179, 433. 

CAVALIERE A. (1979), "Proceedings of the IAUPAP Conference on Cosmic Rays" 
(Kioto) . 

HAZARD C. and MITTON S.(1979), Active Galactic Nucle i , Cambridge University 
Press. 

GELLER M. , TURNER E. and BRUNO H. (1979), "Ap. J. (Letters)" 230, LI 41. 

PACINI F. and SALVATI M. (1978), "Ap. J. (Letters)" 225, L99. 

PACINI F. and SALVATI M. (1979). In preparation. "Physica Scripta" ( 1978) , 
17, 3. Quasar* and Active Nuclei. 

REES M. (1967), "M.N.R.A.S." 135, 345. 

SETTI G. (ed.) (1977), Physics of Non-Thermal Radio Sources , Reidel. 

WOLFE A. (ed.) (1978), BL Lac Objects, University of Pittsburgh. 



275 - 



ALFONSO CAVALIERE** ) 



PHYSICS OF THE COMPACT SOURCES IN ACTIVE 
GALACTIC NUCLEI AND QUASARS 

1. INTRODUCTION 

The phenomenology sketched in the previous talk (see also 
Appendix) implies three main as trophysical problems: the nature 
of the primary energy source; the factors that drive the strong 
density and/or luminosity evolution of the quasar population 
over cosmological time-scales; the physical processes that gen- 
erate and radiate in quite compact volumes the prodigious power 
in continuous electromagnetic radiation emitted by these ob- 
jects. 

It is my purpose to show that the essenti als of the physics 
underlying all these problems can be pin down by straight im- 
plications from the observational data, independently of any 
detailed (and uncertain) modeling; and that much additional 
structure is strongly indicated - to. say the least - when the 
data are related by, and referred to, general astrophy si cal con- 
siderations. I shall conclude with some implications, which how- 
ever hinge upon two' specific assumptions, concerning the role 
of high energy protons producing y-rays and neutrinos that may 
be observable in the near future. 

2, THE PRIMARY ENERGY SOURCE 

A. The Role of Gravitational Energy 

The life-time of the Seyfert activity can be reliably es- 



(*) University of Rome and Istituto Astrofisica Spaziale, C.N. R. , Frasoati . 



276 - 



timated from the statistical occurrence of Seyfert galaxies; a 
few % of all spiral galaxies; thus the total energy output is 
Lt^lO erg. For Quasars, values up to 10 erg obtain (Schmidt 
1971). Any nuclear burning - the stellar energy source - can 

2 2 

convert only < 10~ Mc , and thus it is certainly irrelevant in 
sources with L^ 5 /Ri S > 1 when compared with the gravitational 

2 

energy GM /R liberated upon gathering the same mass within the 
size R. The condition for gravitational energy to be dominant 
reads expli cit ly L 4 . s te/Ris > l ■ The mass involved is M 3 =r}~' 2 (L 4 . s t a R is) 2 
if 7) is the overall efficiency for conversion of the gravita- 
tional energy released, into the radiation observed. 



B. Modes of Ener gy Re lease 

Several alternatives still linger undecided," as for the 
specific modes in which such a release and conversion may take 
place; they share common features, however, in their essentials 
and outcomes. 

A strong observational clue is provided by the presence 
in many associated radio sources of distinct linear structures 
that are co-aligned in each source over scales ranging from 
under a pc to several Mpc (see e. g.Kel lermann 1978 ); di rection- 
ality and long-time memory thus exhibited can hardly hinge on 
anything but the angular momentum J of a coherent massive ob- 
ject. 

On the theoretical side, the specific angular momentum j 
of the mass involved must exert some control over the rate of 
energy liberation; a smaller j implies simply that the centri 
fugal barrier to the collapse ( rotational energy W=Y 2 fMR H ~fl" 

2 

matches V=gGM /Ron con traction, provided that R > R , the radius 
of the event horizon) is reached in a more compact -hence a more 
powerful - configuration. 



2 



4-6 15 8 

(*) Notation: L = 10 t 45 erg/s, R = 10 Bxscm etc; , including M = 10 M e M & (so- 
lar masses ) . 



- 277 - 

The simplest possibility is constituted by a self-gravi- 
tating magnetized plasma body (spinar: see Morrison and Cava- 
liere 1971, Cavaliere, Morrison and Wood 1971; magnetoid: see 
Ginzrburg and Ozernoy 1977 and bibliography therein) that col- 
lapses gradually under the control of its own j, in conditions 
of rotational equatorial support: 2W + V ~0. The magnetic field, 
intensified during the contraction by flux (q>) conservation, 
not only provides internal axial support, but also with its out- 
ward extension sets up a large scale, rotating configuration 
of magnetic and (induced or electrostatic) electric fields; the 
basic electrodynamics is similar in many but not in all res- 
pects to that in a Pulsar's magnetosphere and has been redis- 
cussed many times, since Cavaliere 1969, Morrison and Cavalie- 
re 1971. It turns out that these fields remove J at a rate 

— - = - — n( — (2.i) 

dt c \ c J 

which is remarkably independent of assumptions concerning axial 
symmetry of B (it depends only on the polarity of the poloidal 
component: m=0 corresponds to a quasi -radial structure, m = l to 
dipolar etc.), and is independent also of the ( charged) particle 
density in the body's magnetosphere. For an approximately rigid 
rotation, a power P =JQ must be emitted, in very long wavelength 
e-.m- or Al f ven waves, or most likely in relativistic particle 
winds; alternatively, P may be viewed as the integral flux of 
the Poynting vector outwards of the critical surface where the 

2 2 

corotation velocity reaches c: P=cR B . In terms of the observ- 

' c c 

2 2 - 1 

ed L=7)P,the requirements are fixed by B±M B = 0.3 rj r L 4S , where 
7j is the efficiency for conversion of large-scale e.m. power 
into radiation; the example of the Crab Nebula shows that Tj r 
may well approach 0.5. Removal of J allows further gradual con- 
traction: R=R (1- t/ T o) m * with an attendant luminosity in- 
crease L/L '(R/R )." (3 * m - ) = (l-t/T )- 1/P, p *(2+m)/(3*myZl;' the 

- P Q 

initial time-scale is t ^L q , of order 10 yr at the level of 



- 27 8 - 

42 

10 erg/s. Small scale instabilities would not materially clog 
the mechanism. A final dimming and a cut-off must be expected 
either by flux loss or by final collapse to a Black Hole con- 
figuration. 

Alternatively, the potential well may be provided by an 
already formed Black Hole, and energy may be released by a mass 
inflow from an external supply torwards the horizon at 
R s =3 10 M a cm: the requirement is M=10~ rf L 4S Mq yr~ (Rees 
1978 and bibliography therein). For large j, a classical ac- 
cretion disc may form, where j is transferred outwards (yet not 
removed) by dissipative viscosity ; thus the internal shells are 
allowed to collapse further towards the horizon, and to convert 
more gravitational energy into thermalized power. The configu- 
ration is known to be unstable, and the maximum temperature is 
too low when M^IO-Mq (a point discussed further in Sect. 4). 
The magnetic viscosity invoked (the collision - dominated vis- 
cous stresses falling short by orders of magnitude) is likely 
to be ineffective inside the disc (Galeev, Rosner and Vaiana 
1979), so that effects of a turbulent external B have been ap- 
pealed to so as to produce a hot corona (Liang 1979 and refer- 
ences therein). Blandford 1976 and 1979, has stressed instead 
that the large-scale external structure of the B field threaded 
into each shell of the disc, can behave much as in the spinar' s 
case, with analogous global results: P 45 ^ B A M e , mainly focussed 
in the axial direction. Blandford 1979 also summarizes other 
more exotic, and not yet fully explored, mechanisms for energy 
extraction from a rotating Hole. 

If mass flows in with, a small j, a quasi -spheri cal accre- 
tion flow may prevail (Rees 1978). With a low initial dissipa- 
tion, the gas would heat up almost adi abatical ly to reach in- 
teresting relativistic electron energies, where rapid cooling 
processes set in. This accretion mode, however, en tai Is J=0 and 
turbulent Bjthus it would nat be easily related to directional 
phenomena in radio-sources , nor to the high optical polarization 
discussed in Sect. 4. 



279 - 



In any accretion-driven source, it is the external gas 
supply that ultimately controls the output L: it is not clear 
that the Eddington limit Lg = 10 M B erg/s should be really 
relevant (Rees 1978), nor that the observed L do not actual- 
ly exceed it. The gas lost by stars throughout the body of a 
surrounding galaxy is all too easily dispersed by Supernova- 
driven winds, or ablated by . ram- pressure exerted when the 
galaxy moves through an intracluster medium, before getting in- 
to the nucleus (cfr. Frank 1978, Gunn 1979). A more suitable 
supply is constituted by the stars in a dense cluster around 
the central Black Hole, when they are disrupted by tidal effects 
as they pass by the Hole or as they collide between themselves. 
Frank 197 8 assesses the results of much research in this field: 
tidal disruption, essentially at the "n<Tv rates", can provide 
mass inflow at a rate M 4 0. 4 JfJJ (t ^ 7 1/2 fl~ *■ <* 10'* M& yr' 1 (R c 
is the radius of the core of the star cluster in pc,N 7 the star 

7—3 

density in 10 pc and Mu is the Black Hole mass). For higher 
densities, necessary to explain L > 40 erg/s, star collisions 
dominate and M<10 N 7 fl pc % yr obtain. Explicit time his- 
tories may be computed using as a guide the results for homol- 

5/2 

ogous contraction (Lynden-Bell 1975) that read NR ^const and 

4/7 
R2tR (l-t/T ) (t q *40 r R , r R being the two-body relaxation 

time, again goes inversely with L); numerical L(t) have been 
computed by Young, Shields and Wheeler 1977. All results show 
a sharply rising L(t) ~ (l-t/r )~ /p with p <1 uptoa final cut- 
off, with time-scales t of order of a few to several 10 yr. 



3 . THE QUASAR EVOLUTION 

The very fact thatQuasars as a population evolve, requires 
the Quasars phenomenon to be short-lived on the average, r< H Q , 
and to be associated with a particular cosmological epoch: z £,2- 3 ; 
formation soon after collapse of the protogal axi es to their pre- 
sent configurations is the canonical option. Any structure in 



- 280 



the data must imply a specific feature in the distribution of 
the actual t' s around t. 

An invariant formulation of the governing factors involved 
can be given on taking up and extending the pioneering consi- 
derations by Cavaliere, Morrison and Wood 1971. 

A population evolution must be governed by a conservation 
principle: N(L, t) , the comoving density of sources per unit to- 
tal luminosity interval at the cosmological epoch t, must obey 
the continuity equation 

B/V B . 

r- + r- (LN)=o (3.1) 

Bt BL 

The factor L(L,t) describes the individual evolution of 
the sources; technically, the trajectories in the-L, t plane 
defined by the equation L=L (L, t) are the characteristics of the 
partial differential equation Eq. (3 . 1 ) ; they guide - as i t were - 
the flow of N(L,t) in the L, t plane, and thus control the main 
features o£N(L,t) with their qualitative behaviour ** ^ . 

The latter, in turn;is fixed by the gravitational nature of the 
primary energy source , which implies (Cavali ere and Messina 1980): 

a) By gravitational contraction - i.e. overwhelming self-gra- 
vitation - the system is dynamically secluded from the out- 
side world: the evolution becomes a local affair governed 
by an intrinsic scale provided not by t, but rather by L it- 
self. Technically, the autonomous character of the equations 
for sel f-gravi tation will be reflected into a form L =L(L). 

b) The basic accelerating trend of sel f -gravitation , once set 
in, only temporarily can be checked by the effects of angu lar 
momentum. Inevitable loss or dispersion of the latter will 
eventually let free this accelerating nature, while in turn 



(*) This control is actually so strong that even a source term on the r.h.s.' 
of Eq, (3.1): S(L , t) ?0 for low L, does not change the asymptotics of 
N(L,t). 



281 



loss and dispersion rates will increase as the contraction 
advances (see Sect.2). 

One expects then, mode I- independent ly: 



L = AL 



P + i 



or 



L = 



1 - 



t-t. 



J/P 



(3.2) 



with p>-l, and r a 1/p A L , where t is the epoch of core for- 
mation and Lq their initial luminosity. A physical cut-off will 
obviously prevent the final divergence formally appearing in 
Eq. (3.2); this will be insured in specif ic models ( see Sect.2). 
The important, general feature of these characteristics is that 
they diverge in the L, t plane so that the flow of N(L,t) they 
guide must show rarefaction towards increasing t and L.In fact, 
the solution of Eq. (3.1) is a joint distribution 



N(L,t) = 



L 



P+i 



N [Lo(L)], 



(3.3) 



which asymptotically, for p A L At » 1 , goes into a separable 
form 



N(L,t) 



P+l p+1 



Nr 



( P At) 



1/t 



F(L)xg(t) .(3.4) 



that predicts density. evolution for high L and t. 

In this regime, a luminosity function F(L)=1/L results 

from the equilibrium between inflow of sources into the region 
of fast evolution, and their drift towards large L; the index 
p is expected to take on values p £.1 ( cf r. Sect. 2). F(L) carries 
direct information about the individual evolution. The rate of 
evolution, with its detailed behaviour, tells instead mainly 
about the distribution of L , and hence about the basic para- 
meters that determine it '.- I f N Q (L Q ) ~£q for. small L , then the 



- 282 - 

time -dependent factor g(t) in Eq . (3 . 4) becomes g(t) ~ t , 

i.e. monotonically decreasing towards large t ( '. But it is 
easily shown that it has a plateau, or a maximum at some t near 

a 

t , because N (L ) ~Lo must hold at large L , with |3 > 2 for 
convergence. 

Now, for any gravitational energy supply, L will go in- 
versely with the radius of the mass stockpile (this is borne 

- k 
out by the specific models in Sect. 2): Lo^Ro . Once again, 

the specific angular momentum jo is one important controlling 

parameter: if at least initially rotational support prevails, 

/Mflo- gGM/Ro, thenfio^Jo. so that 

•2k 
L ~ Jo . (3.5) 

and N(L ) =N(j )dj /dL applies. But in any case fMR Q £l 4 gGM/Ro 
must hold for any interesting collapse, and thus the active cores 
must satisfy j-$jomax = (gfG) (3/iHT) M p , where p is 

1/2 

the initial density. In addition, j > j ' m . =(2g/f) GM/c must 
apply if R > R is to hold. Taking also account of the distri- 
bution of the core masses M, the distribution N(Lq) is expected 
to rise sharply with increasing Lo to reach a maximum before 

- 2 

the final decline which must be faster than L . 

To summarize, the gravitational nature of the energy supply 
implies divergent characteristics, thereby a rarefaction flow 
of N(L, t) and a density evolution at high L, t; the controlling 
influence of the angular momentum entails monotonical increase 
of source density in look-back time, up to an inevitable plateau 
or maximum. Aj,l quite consistently with the trends of the data. 



(*) The evolution may be expressed in terms of the redshift z using, for 
Friedroann models, the translation 

dt 1 i 

1 1 

when the density parameter CO = 1 t °* obtains ;when CD^-0, t~ — . 

fl + z> 3/2 ^ 



- 283 - 

In addition, the strong dependence r ~L P ~y P implies that 
at constant M, the average cores in spiral galaxies, being pre- 
sumably endowed with a high ;', should reach an activity climax 
weaker and later than cores in elliptical galaxies - not unlike 
the features of Seyfert activity (Weedmari 1977). 

4. PHYSICS OF THE RADIATION SOURCE 

A) The Problem with the Energy Supply 

The conventional alternatives for continuous emission are 
constituted by "thermal" radiation processes (photon energy 
hv?i<e>, the average electron energy) and "non -thermal " pro- 
cesses (hv«e); the antithesis, however, may be somewhat mis- 
leading for sources in AGN. In fact, their high luminosity 
(L>10 erg/s, up to 10 erg/s) and small size (R ^ c^t ^10 15 cm) 
make up a high energy density w = L/UttR* c ^3 10* 'z. 4 5 / R\ 5 , and a 
high photon density N ph =w/hv = 5 iO^L^s/flis^i s , far exceeding 
the particle density: this "photon barrier" makes electron- 
photon, and even photon-photon 1 , interactions more important than 
the particle-particle interactions. 

The probability for any electron to collide with a photon 
within the source is very large for L 4S /# 15 > 4 : 

T ey =<r T wR/hv= 3 iO S L 45 /i? ls v 15 (4.1) 

Then the electrons must freely exchange energy with the 
photons by frequent scatterings y+e=y'+e', and a considerable 
fraction of the total radiative power may be upgraded to max- 
imum energies of order of electron energy, hvcas: from IR - 
band up to high energy X-rays or even y-rays. 

In a truly compact source, the upward drift in energy will 
be halted at hv^.1 MeV by the effects of pair creation y+y=e + +e~, 
with probability (hv^hv'^0.5MeV) 

r rr =<T^fl^L 45 /fl 15 ; (4.2) 



284 



this process degrades photons emitted at larger energies (Ca- 
vallo and Rees 1978) before they can leave the source. The 
threshold condition is hvhv' ^2(mc ) ; thus y-rays can interact 
even more with the more numerous lower energies X-rays: in other 
words, if the spectrum of 3C 273 does indeed extend to 100 MeV, 
then the J- ray source cannot be smaller than some 10 cm (Fa- 
bian and Rees 1979). On the other hand, in sources that are not 
too compact the scatterings could proceed up to their intrinsic 
cut-off set by hv <e (for inverse Compton interactions, this is 
just the Klein -Nishina limit). 

2 

The next important point concerns the ratio e/mc ~y. Ob - 
servations of several objects emitting high power into the 10 
keV range, tell directly that the electrons must be at least 
weakly relativistic. Other observations suggest strongly that 
in many objects- conditions far from equilibrium must prevail, 
including specifically powerful production of highly relativ- 
istic electrons. For one, the high linear polarization of vio- 
lent QSO' s, and especially that of Lacertids which is defini tely 
outside the limits obtainable with simple scattering ,indi cates 
Synchrotron emission in the optical band, or alternatively the 
action of differential propagation which discriminates between 
different polarizations : bo th effects require a well ordered ma- 
gnetic field geometry. Further, the compact radio -emission as- 
sociated with several AGN implies again Synchrotron emission 
and thus powerful production of relativi stic electrons (Keller- 
mann 197 8). As to the y-ray emission from 3C 273 , on a thermal 
interpretation it would require, implausibly, relativistic tem- 
peratures T^IO °K produced in a region very far from the ac- 
tivity center, r ^10 R s , 

Finally, the observations also impose the constraint that 
the particle density must be low within, or just outside of, 
the radiation source (Blanford and Rees 1978) . Specifi cal ly , 
one condition is r =CTy n R <1; for, a high probability of Thom- 
son scattering would cause the photons to diffuse throughout 



- 285 



the source: any sharp time variability at the emission would be 
smeared out or slowed down ( ',and the spectrum would be moulded 
into an incipient black -body shape. In addition, in the presence 
of magnetic fields a second condition must hold: the Faraday 

2 2 

rotation should be small, *p B =47Te Rnv B / Icmv^v <1 , to conserve 
any net polarization at the emission. 

As for interpretations, thermal scenarios assume a plasma 
heated up at T<,5 10 °K on its way down the horizon of a mas- 
sive Black Hole; however, the classical, purely thermal accre- 
tion discs would be too cool: T ~ 5 10 7 (M/M )' 1 ; thus, even 
starting from a thermal framework one is forced to admit energy 
liberation via twisted (turbulent) and ampli fi ed magneti c fiel ds 
that "flare" and dissipate their energy (Maraschi et al . 1979, 
Liang 1979) by accelerating particles. In these conditions, a 
thermal redis tribution of particle energy is hardly consistent, 
because of the high temperature kT^mc that makes the colli- 
sional cross-sections quite smali.and because of the low elec- 
tron density. To take account of the bound on n , r <1, the 
electron relaxation time (the shortest one) is best written as 

* 5 10 3 Tl ° RlS (4.3) 

Furthermore, the density of radiating electrons being thus 
limited, their cooling time t =<e>/l (I = radiated power per 
particle) becomes very short at high luminosities 

t = =10 7- . (4.4) 

r .2 ccx T W r* i + 5 

The ratio of these two times reads: 




(*) The ingenious proposal of reflection scattering by Lightman and Rybicki 
1979 faces a similar problem at high frequencies. 



- 286 



ee „ . MO 1.48 f a C\ 

^ 0. 5 (4. 5) 

t ' / Sl5 

r re 

When 44B^Bi5 ~ 1 , the energy is radiated faster than it 
could be redistributed via collisions: maintaining truly 
thermal conditions in the source in the face of the enormous 
energy flux required, is a major problem.- One may appeal to 
enhanced, collective relaxation and transport phenomena: these 
have yet to be specified in the present context, and their 
effectiveness in checking the particle distribution functions 
(while transporting the large energy flux required) is to be 
ascertained. • 

The alternative is to accept that particles pick up power 
directly from the e.m. fi elds and indeed run away in energy be- 
fore sharing it with other particles; the radiation rate will 
be the ultimate limiting factor. 

In a conventional non-thermal scenario, the relativistic 

,2 

electrons lose energy to photons in the amount de/dt = -y cr^Yf, 
that is,Ae/e = y hv/jmc per scattering event; the cumulative 
loss turns out to be formally very large whenever L 4 5/f?i5~^ : 

Ae 
r =r v — -= yL 45 /fl 15 »i. (4.6) 

From the photon viewpoint, the corresponding energy gain 
and redistribution constitutes the inverse Compton (IC) radia- 
tion; and Eq. (4.6) means that the electron radiative life-time 
t s roc 2 /yo-yYI is bound to -be much less than t ( .-R/v ] the elec- 
tron crossing- time through the source at a velocity v<c, b 



t It < t c/R = r- x «1. (4.7) 

r' c - r 

Catastrophic energy losses thus prevail. In fact, these re- 
lationships include also the case of Synchrotron (S) emission and 



- 287 



the associated energy loss: the process can be viewed at as 
scattering off virtual photons of individual energy "(iv> B =heBi /mc 
and energy density W = W g = bI/4tt. The optical depth is 
r fl = cr T W B &s/shv B >yL 4 . s /R 15 since S radiation takes over from IC 
radiation when W g >L/4nR 2 c, and agai n '* r /* c « 1 obtains, the 
condition for catastrophic losses. 

Continuous injection of fresh high energy electrons - an 
easy way out in theories of radio -sources -will not help here, 
because the spent electrons would accumulate and may easily 
violate the constraints r yg < 1 and ^ B < 1 (Blandford and Rees 
1978). 

The conclusion is that replenishment of the electron en- 
ergy is the key problem with the strong, variable sources, in- 
dependently even of the origin of the radiation. Radiation pro- 
cesses involving high y electrons are indicated, but the con- 
ventional S, IC and Synchro - Compton (the same electrons radi- 
ate S photons and scatter part of them to higher energies) re- 
quire reformulation. 



B) A Solution: Extreme Non-thermal Radiation 

Two viable solutions have been proposed, not necessarily 
alternative. The demands on power and time scale can be lowered, 
assuming that in a fraction of all sources a jet of radiating 
particles moves in a narrow (~10°) beam towards the observer, 
with a relativistic bulk velocity corresponding to a Lorentz 
factor y b ZiO: in the jet proper frame the power emitted is de- 

-2 

creased by y b and the associated time-scales are increased by 
y h (Blandford and Rees 1979). The at traction of the idea is that 
jets are indeed observed in many objects in the radio and op- 
tical bands, and constitute a likely explanation for the super- 
luminal effects detected in microwaves (Readhead and Scheuer 
1979). One possible drawback is that in these conditions the 
variability time scales should be in versely correlated with the 
apparent luminosities, whereas a time scale of i&l day is ob- 



288 



served over a wide range of luminosity (Moore et al. 1980); a 
specific and extended body of data is needed to clarify this 
issue. Still, the low efficiency of an el ectron -proton jet may 
pose a problem: an e -e~ plasma may be needed (see Sect. 5). 

Another solution is to cope with the demands by using con- 
tinuous electron recycling; this has been recently discussed by 
Cavaliere and Morrison 1980, see also Cavaliere 1979, to which 
we refer for details and bibli ography. The basic idea is to ac- 
cept and tackle at once both continuous reacceleration of the 
electrons within the source and the limi-ting effect of the ra - 
diation on the electron energies. Each electron is re-cycled, 
as it were, a number of times N » 1 ; the maximum value N^t c /t r 
corresponds to "continuous" reacceleration .On can convince him- 
self that to this condition the electrons will tend in the pre- 
sence of an energy gain rate p ( r,) , finite throughout the region 
were the radiative losses I =e/t r also occur: consider the 
simplest geometrical set up, a spherical shell with radius ft 
and thickness Afi ~ft crossed by a flux f=Unr nv = const of elec- 
trons at a velocity v ( the simplest extension of the conventional 
Synchro - Compton process); the energy equations reads 

-11= „ - I (4.8) 

dt 

Clearly, when the losses grow steeply with J they soon must 
strike a balance with the gain such that de/dt 0*0 or, when 
I _=a T cWy* (S or IC losses) 

P (4.9) 



7 = 



cr~cW 



Equivalently, this condition may be written t r ~t a (t a ~e/p 
being the time-scale for acceleration), to stress that in this 
extreme non -thermal process the radiation rate is controlled by 
the acceleration rate. Thereby an important constraint becomes 
apparent: t cannot be arbitrarily small, rather it has the 



- 289 - 



lower bound t--t„; hence the upper bound N=t It =t It obtains 
ru * * c r c a 

(it will be seen that N^IO ). This implies a lower bound for 

n, because.by energy conservation in steady state, L = feN holds. 

With this density, the source remains thin to Thomson 

~ . 2 2 2 

scattering: T g 2sL/efl By , even if the electrons eventually 
cool down to subrelativistic energy. The Faraday rotation at, 
or immediately outside, the optical source may be critical , ins- 
tead: 



»C \ V J 



L t eB 

** a ~71 "i - (~J (4 - 10) 

C R*B 2 y nt 



Moreover, the radiating electrons will perturb the ambient 
magnetic field in the source, by an amount measured by: 

2 L * r c B 2 

n-ymc = (4.11) 

cR 2 B 2 t c v k-n 

Eqs. (4.9) and (4.10) may require a source structure such 

2 2. 

that L/cR B is never too large, or even is £ 1 (on the other 

2 2 > 

hand, L/cR B ~ 1 is the source condition for 5 emission in par- 
ticular to be responsible of the polarized radiation). And we 
may recall that high polarization requires, independently of 
any specific radiation mechanism, strong order in the ambient 
magnetic geometry. 

These requirements would be jointly satisfied in the sce- 
nario of a massive plasma body holding a strong B field, and 
rotating so as to generate coherent electric fields. The plasma 
may be either sel f-gravi ta ting or accreting in a disk-like con- 
figuration toward a massive black hole (see Sect- 2); in any 
case, its slow contraction transforms gravitational into rota- 
tional energy, and finally into the Poynting vector flux cB R. 
associated with large scale B and E fields. The large-scale 
Poynting flux thus converts energy from the gravito-ro tational 
machine, and at the same time transports it to the radiation 



- 290 - 

2 2 

source; the related efficiency is given by L/cR B <$i. 

In the extreme non-thermal process the electrons will ra- 
diate both in the S and in the IC modes; the respective fre- 
quency ranges are identified in magnitude by 



v „ ~ y 2 v R ~ 5 10 B 2 y 2 



v r ~ y v„ ~ 5 40 6 2 72 



(4.12) 



and the relative strength is L^/Lq = ^s/^vh' *-^° m hining the Eq. 
(4.9) with the energy conservation in the form L = fpt , yields 



L 45 =i0" 1 n 5 i?i 5 Bl72 (4.13) 

Thus the parameters y, n, B can be fixed on the basis of the 

2 5 3 2 3 

data to obtain: y^lO , n^lO cm. and"B~10 -10 G in the ra- 
diation region. 

It is also part of the picture that the emitted spectra are 
sustained, in spite of the fast losses, by continuous energy 
pumping. This means that Eq. (4.9) fixes local value of y(r) and 
hence of v~(r), v„(r) once p(r) and W(r) are given. Now, B(r) 

will go like r (m = quasi -radi al , m=4 dipolar etc.), while 

- 2 
W(r) ~r when the radiation dominates. Thus the emitted fre- 
quencies v s (r), v„(r) will increase outwards; one may well ex- 
pect that more "extended" acceleration (p(r) more nearly cons- 
tant across the source) will produce more power at higher fre- 
quencies, that is, flatter spectra and enhanced IC radiation. In 
fact, the idea of an acceleration process continuously acting 

1 ±6 

throughout the source can be made explicit by setting p(r) ~ r 
(e&l)> then the spectral behaviours can be derived simply from 
energy conservation in the form 



L -./. dv'L(L') = f I dr'p(r') 



291 - 



The resulting S spectra have slopes around 1, speci fically 
a = 2m/(2m\e) ; while the IC spectrum turns out to be flatter, 
with slope S~0.5. These results agree with the observed be- 
haviours; added details and comparison with the data may be 
found in Cavaliere 1979 and Cavaliere and Morrison 198 0. 



5. HIGH ENERGY PROTONS AND THEIR PRODUCTS 

In non-thermal cores of AGN, protons are likely to be ac- 
celerated by the same or by equivalent e.m. configurations as 



the electrons, up to energies £ p = e (or £ p = (m p /m e ) e if the 
acceleration is e.m. rather than electrostatic, cf. Salvati 
1975 ; the same factor will carry through all the energetics). 
But the electrons suffer extreme radiative losses as previously 
discussed, while the protons do not; thus the bulk of the pro- 

2 3 

tons will reach terminal energies of order £ ZiNs %10 x 10 MeV. 
If protons constitute the main positive component that insures 
overall charge neutrality, the source will produce a proton out- 
put L ~L ; however, it is conceivable that positrons instead 
may constitute the main counterparts of the radiating electrons: 
such condition will prevail when and where y+y-or y.+ e pair 
production operates. In the assumption that protons dominate, we 
proceed to discuss possible observations bearing upon the pro- 
ton role. 

GeV _ protons may reveal themselves through 100 MeV y-rays 
emitted on interacting with the diffuse gas known, from the 
emission line spectroscopy, to surround the active cores at 
r^lO cm, filling a volume fraction F ~ 10 with a density 
n^l0°cm' 3 . The branch p +p =.. -.77° -»2y (cross-section a ~ 10 
e X ' 2 GeV for B p £ 1 GeV) produces a y-ray output L y ^L p anR p F v , 
Efficient use of the protons requires that the small factor F^ 
be compensated by an effective proton path length R p ^10 r; 
this second assumption is in fact likely to hold true, consider- 
ing the gyro-motion around the B lines, the winding of the B_ 



- 292 - 

lines themselves (a toroidal configuration prevails at large 
r), and the final diffusion motion between the gas filaments. 
The 7T° -*2y spectrum is flat in the £ 100 MeV region, cf. Ginz - 
burg 1973, certainly too flat to fit the available data points 
on 3C 273 that indicate F(v) ~v -1 ' 7 from 50 to 800 MeV; how- 
ever, the contribution by electron relativistic Bremsst rahlung 
may fill in the range 10-100 MeV. These nuclear y-rays are not 
expected from Lacertids if they really are deficient in sur- 
rounding gas . 

The proton energy distribution should extend to much higher 
energies in the absence of fast losses during acceleration, In 

2 3 

the energy range 10 -10 GeV the pp interaction produces, via 

the branches p + p = - ■ .tt° -* 2y and p +p=r. . tt^.—v, j7+ / u ± -* e ± +v+v, y-rays 

and neutrinos (of all kinds) in about the same number and with 

closely similar .energy distribution , sensiti vely related to the 

distribution of the parent protons when N ~S with s ^2 to 

r p 

2.6: neutrino and y- ray observations may thus provide comple- 
mentary probes of the proton acceleration and radiation pro- 

6 2 1 

cesses (Fichtel 1978). For example, a flux of 10' ph cm' s~ 
at hv^lOO MeV (a level currently detectable) implies 3 10' 

"2 3 2 

neutrinos/ cm. s at e v ^10 GeV if s = 2. 6, and 10 as much if s=2.2; 
such fluxes would be detectable by currently contemplated pro- 
jects for neutrino astronomy like DUMAND, which envisage a de- 

1 — 1 2 1 

tection threshold o$2fl0ct yr~ equivalent to 2^10 erg cm' s~ . 

The minimum detectable sources will have luminosity L and dis- 

- 1/2 1/2 

tance D related by D £.30 L VAS £ Mpc , £ being the percentage 

of L v within the DUMAND dynamic range, £—1 for s = 2.5 (Eichler 
1979); recall that L v %L when L XL. Note, however, that the 
pp interactions produce a comparable power in e , with an en- 
ergy distribution peaking at ~ 100 MeV (Ramaty and Lingenfelter 
1966); in the magnetic field existing at r Z>10 cm, these elec- 
trons would radiate a S spectrum peaked at vo?5 10 B and ex- 
tending to high frequencies which would be rather difficult to 
(re)absorb entirely: candidate neutrino sources shou Id be marked 



- 293 



not only by. •y-ray but also by an appreciable radio -microwave 
emission, and this condition would exclude most 'Sey f ert type 1 
(like NGC 4151), very weak in this band. 

APPENDIX: CRUCIAL OBSERVATIONAL DATA 
CONCERNING ACTIVE GALACTIC NUCLEI (AGN) 

A few % of all galaxies exhibit obvious peculiarities at 
their centers: most conspicuously (Seyfert galaxies), a small 
overluminous nucleus, and a spectrum rich in strong, high ex- 
citation emission lines (cf. e.g. Osterbrock 1978): the spec- 
troscopic analysis has provided a composite picture of gas 
"clouds" and filaments extending with decreasing density and 
velocity outwards of some 10 cm from the activity center. It 
is the continuous radiation from the inner core, however, that 
tells more directly about the central powerhouse and conversion 
machine, by its unusual features: extremely wide spectral ex- 

» . . . . 44 

tension, from radioband to X-rays; high in tensity, o f ten L > 10 
erg s , outshining the main galactic body ; variabili ty on time 
scales of months to under a day, which indicates by the simplest 
light travel-time argument source sizes R^cAt down to 10 cm. 
BL Lac type Objects continue the trend of the violently variable 
QSOs in most respects, except for lacking almost entirely the 
emission spectrum (cf. e.g. Strittmatter 1978 ) . Obj ects of both 
classes have been shown to be surrounded by galactic images 
(Kristiah 1973, Gunnl978). 

The prevailing view is that Seyfert galaxies Type 2, Type 
1, QSOs and Lacertids constitute a sequence of AGN marked by 
the increasing dominance of the direct core emission over that 
from the galactic body, and also over the radiation reprocessed 
by the surrounding material: gas forming the emission lines, and 
dust re-radiating thermal. IR (Neagebauer 1978). The energy pro- 
duced by these sources is estimated, from their life-times in- 
ferred on the basics of statistical frequencies relative tonor^ 
mal galaxies, -at 10 -10 erg (Schmidt 1971). 



294 - 



The radiation is "compact", compactness being measured by 
the ratio L/R: values of L£iO ergs" and cAt 2s 10 cm are 
statistically f requent . Reco rd breaking examples have been pro- 
vided by the outbursts of the Lacertids AO 0235+164 (Rieke et 
al. 1977) and B2 1308+326 (Moore et al . 1980) both with 

47 - 1 

jLtdq — 5 10 ergs , varying by 50% in a few days. In X-rays, 
NGC 4151 varies by a factor of 2 in 1.5 days (Mushotzky et al. 

44 - 1 

1978); OX 169 with L ~i0 ergs' varies by a factor of 3 in 
2 hours (Tananbaum et al . 1979). 

The output is concentrated with remarkable uniformity in 
the IR -0 band (5 1Q 1 * to lQ 1B Hz) and in X-rays (5 10 17 to 10 2 °Hz) ; 



the spectral shape may be approximated roughly by two power 
laws F ~v , with a slope often steeper in the former region 
(<x£i) than in the 1 atter (« ~0. 5 beyond a few keV) (Mushotzky 
et al. 1979). 

A dominant y-ray emission, L ~2 10 ergs at' ~ 100 MeV , 
has been detected from 3C 273 (Swanenburg et al.1978). The MeV 
emission by NGC 4151 is more con trover si al , but clearly the ob- 

4 4 1 

j ect emits most of its established output (~20 erg s ) in hard 
X-rays (Delia Ventura et al. 1979). Emission in y-rays at le- 
vels L^> L , however, must be statistically infrequent , in view 
of the upper bound set by the y- ray background (Bignami et al. 
1979). 

Linear polarization in the and near IR is high (up to 
30%) in many Lacertids, relatively v- in dependent , and rotates 
rapidly in At^lO h (Stein et al. 1976, Moore et al. 1980); a 
number of violently variable QSOs show similar, if scaled down, 
behaviour (Visvanathan 197-3, Stockman and Angel 1978, Knacke 
et al. 1979). 

The radio emission from the cores (some direct interfero- 
metric limits r^.10 cm have been obtained) in many Lacertids 
and in a few QSOs amounts to a sizeable fraction of the total 
output. Brightness, spectrum and polarization are consistent 
with Synchrotron radiation; the associated output in relativ- 
istic electrons is even larger (see e.g. Kellermann 1978). 



- 295 - 

Population evolution of Radiosources (including radio -loud 
Quasars, a minority of 1-10% of all Quasars) has • long been re- 
cognized from the "excess" of low flux sources, N(> So) ~5d ' 8 
as compared with the Euclidean, constant density case, N(> S R ) 
flatter than S R ' . Optically selected Quasars have shown an 

_ 2 

even stronger evolution, N(>S Q ) ~ S or somewhat steeper 
(Schmidt 1978, Braccesi et al_ 1980). Evolution in the X-ray 
band is being revealed by deep surveys conducted by HEAO - 2 
(Giacconi et al. 1979, Cavaliere et al. 1980). 



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, - 299 - 

NICOLA CABIBBO 
CONCLUDING REMARKS 



Recent advances in astrophysics as well as in particle 
physics have rekindled the traditional mutual interest of the 
two communities , and this conference has offered a timely meet- 
ing ground for the exchange of information, and the presenta- 
tion of the latest results in the fields of common interest. 

In concluding this exciting meeting, I would like to offer 
a few remarks on some of the many developments which were dis- 
cussed here. 



SUPERHIGH ENERGIES AND THE EARLY UNIVERSE 

The successful development of gauge theories and different 
proposals for a complete unification of the fundamental forces 
has focussed the in terest of particl e physicists on energy ran- 
ges which cannot be investigated directly through accelerator 
experiments. 

In grand unified theories, which were discussed by J. El- 
lis, the nature of the forces between elementary particles is 
expected' to change drastically- at energies near to 10 GeV, 
which exceed by ten orders of magnitude the rosier hopes of 
accelerator designers. At these energies weak, electromagnetic 
and strong forces would fuse into a single unified force, and 
the usual distinction between leptons and hadrons would disap- 
pear. At the unification energy an electron can freely trans- 
form into a quark and viceversa: baryon and lepton numberswould 
not be conserved. 

One could also imagine scenarios where the nature of in- 
teractions changes many times when energy increases from 100 GeV - 



- 300 - 

■ 

where the unification of weak and electromagnetic interactions 
takes place, to 10 GeV, an energy where gravitational inter- 
actions become predominant, even on a microscopic scale. 

One of the main reasons for the renewed interest of parti- 
cle physicists for astrophysics is that, according to the big 
bang cosmology, this wide ran ge of energi es was traversed during 
the initial expansion of the universe, so that relics of the 
interaction law at, say, 10 GeV can be imprinted in the uni- 
verse that we see now. 

This interest is clearly reciprocal, as the knowledge of 
the interaction laws at very high energy is necessary for the 
understanding of Big Bang dynamics. 



PHASE TRANSITIONS AND THE COSMOLOGICAL CONSTANT 

According to the present understanding, during the early 
expansion, matter has undergone a series of phase transitions. 
In the Grand Unified theories the first should occur at a tem- 
perature of about 10 GeV, and corresponds to the breaking of 
the grand- unified group (e.g. SU(5))' into SU(3) x SU(2) x U( 1) . 

After this transition quarks and leptons are distinct. At 
about 100 GeV a second transition breaks SU(2) x U(l) into U(l) 
- the gauge group of electromagneti sm . At these temperature 
quarks still exist as unconfined particles. A third transition 
happens at about 100 MeV , where quarks become bound into hadrons. 

The possible relevance of these phase transitions for the 
thermal history of the universe has been discussed by M. Ruder- 
man. 

One of the mysteries of particle physics is the exact van- 
ishing of the vacuum energy densi ty , E . A non zero value for 
E would contribute a term to the energy momentum tensor: 

V ac 

T = e E 

vac *>(iv vac 

so that E would appear as a cosroo logical term in the equa -. 

vac r r 



- 3 01 



tions for the gravitational field, and we know that such a term 

is absent. In the presently accepted theoretical schemes the 

vanishing of ^ vac is not at all natural. As an example, it is 

generally assumed that the symmetry breaking is associated with 

the appearance of non vanishing vacuum expectation values of 

scalar (Higgs) fields. It would seem relatively natural that 

E vac = ° in the symmetric state-, leading to E vac ,?0 in the case 

of symmetry breaking. In fact the opposite is true: E turns 

vac 

out to vanish in the non symmetric vacuum. One would then ex- 
pect that phase transitions a ssocia ted with symmetry restoration 
would lead to non vanishing values of E . The effect of this 
on the expansion history of the universe remains to be studied. 
The puzzle of the vanishing vacuum energy is one of the 
strongest arguments in favour of supersymmetri es. Supersymme- 
tric models do lead naturally to E =0. It is not clear at 
the moment that such a model can be built which gives a satis- 
factory description of the world of particles, but the search 
is continuing and may finally succeed. 



THE HORIZON PROBLEM 

One of the main problems of Big Bang dynamics is the 
"Horizon" problem. The cosmological black body radiation is 
known to be extremely iso tropi c ,only very recently we had some 
positive identification of tiny anisotropes. According to the 
standard cosmological models the radius of the universe has been 
increasing according to: 

R . «t 1/2 

universe 

t being the time lapsed from the Bang. 

If we define Rff or i zon a s the maximum distance covered by 
a signal in this time: 

Ru~ ,,-,„_ = ct 
horizon 



we find 



- 302 



D 

Horizon 1/2 

cC t ' *■ 

R t -0 

universe 



i.e., that the universe was subdivided, near the Bang into 
smaller and smaller non communicating regions. The black body 
radiation coming from opposite di rections in the sky originates 
from regions of the universe which have never communicated. How 
can they agree to look exactly the same? 

A subject of further study is that of the modifications 
of the expansion history of the universe due to the presence 
of phase transitions. Could we solve in this way the Horizon 
problem? 

THE MONOPOLE PROBLEM 

It has been shown by 't Hoo f t and Polyakoff that when a 
symmetry associated with a compact group (e. g. SU(5)) is broken 
to yield a smaller symmetry, containing a U(l) factor (e.g. 
SU(3)x SU(2)x U(l)) particles can arise which behave as Dirac 
magnetic poles. The reason is that there is a large degeneracy 
in the vacuum , corresponding to the different ways in which the 
smaller group can be chosen as a subgroup of the larger one. A 
monopole corresponds to a state where the subgroup chosen is 
different in different directions of space, and the choice can- 
not be continuously deformed to give the same choice every- 
where. The latter condition is met where the symmetry breaking 
gives rise to a U(l) factor. 

A monopole solution would behave as a particle with a mass 
of the order of magnitude of the energy at which the symmetry 
is broken. 

The existence of monopoles is a problem for current theo- 
ries, when connected with the horizon problem discussed above. 



303 



As shown by Kibble it is natural to assume that regions separ- 
ated by more than Rff or i zon at the time of phase transition would 
make different (and causally uncorrel ated) choices in breaking 
the symmetry, so that a certain number of monopoles would arise 
(one every few uncorrelated regions). A recent estimate (Ein- 
horn et al.) leads to a density of monopoles which is far larger 

/v. 9 

(by ~ 10 ) than the best available limits. 

A possible solution , di scussed in Ellis' talk, is that mo- 
nopoles might be confined, and would finally annihi late. In this 
case one would not expect to find residual monopoles in the 
present universe. Another solution would be to delay the phase 

transition, so that it occurs at a larger R„ 

B Ho r iz on 

Remaining in the frame of standard Grand Unified theories, 
this could be achieved by some amount of super cooling (it is 
not clear that one can obtain a sufficient reduction this way). 

Alternatively one could imagine a symmetry breaking pro- 
ceeding in more than one step, the SU(1) factor emerging at a 
lower energy, therefore at lower temperature and larger R a 

r ° Horizon 

Either of these possibi li ti es would lead to a reduced - but 
non vanishing - density of monopoles in nature. It would seem 
important to pursue monopole searches, screening large amount 
of different materials. This could be done efficiently by the 
technique employed by L. Alvarez, in which samples of the ma- 
terial to be screened execute a circular motion along a path 
threading a coil: a monopole in the sample would produce an 
e.m.f. in the coil with a d. c. component. A more elaborate ver- 
sion of this technique made use of a coil with a Jo seph son. j unc- 
tion . 



BARYON NUMBER VIOLATION 

The grand unification would be in many ways similar to the 
unification between weak and electromagnetic interactions which 
should take place at about 100 GeV and which we expect to wit- 



- 304 



ness with the next generation of colliding beam devices. 

Traces of the grand unification should be visible at pre- 
sent energies through Fermi like interactions violating both 
lepton and baryon number, leading to processes such as: 



quark + quark — »- quark + lepton 

The probability of such processes would stand to that of 
normal Fermi interactions in a ratio determined by the respec- 
tive unification energies: a rough estimate would give: 

P (Baryon number violation) 



P (Normal weak interaction) 



Energy (weak -e.m. unification) 
Energy (grand unification) 



= 10' 



Although very tiny, the new baryon violating force would 
lead to the prediction of proton instability with a rate which 
is within the limits of present experimental techniques. In the 
spirit of the rough evaluation given above one would obtain: 



4 8 S 8 3 

r (proton decay) Z r (A decay) x 10 =10 s = 3 x 10 yrs 

More accurate evaluations, discussed by Ellis, lead to 
t (proton decay) =10 yrs. Rubbia has presented and compared 

the different MUD' s (massive underground detectors) now under 
preparation. They could detect proton instability if the life- 

3 3 

time is less or equal than £ 10 yrs. 

As first pointed out by Andrej Sacharov in 1967, the non 
conservation of baryon number, together with the violation of 
CP, could lead to the creation of a net baryon number in the 
early stages of an expanding uni verse. With the advent of grand 
unified theories this proposal becomes of great interest. The 
baryon-antibaryon unbalance in the early universe (at tempera- 



- 305 



ture of few GeV) is, according to the standard cosmology, es- 
sentially equal to the present value of the ratio 

Number of baryons „ _ s 

R = - Z 10 

Number of photons 

a very small number, which could well be produced through CP 
violation together with baryon number non conservation. 

The actual calculation would however require more refined 
knowledge on CP violation at very high energy, and the result 
would depend critically upon astrophysi cal parameters, such as 
the speed of expansion through the phase transition. 

In his talk B.Carr presented an alternative to the stan- 
dard cosmology, in which most of the black -body' radiation, i.e. 
most of the photons in the universe, arise from a first gener- 
ation of stars, which he calls protostars. In his proposal the 
baryon number unbalance would be substantially larger than the 
present value of R. 

The possibility of giving an explanation for the predo- 
minance of matter over antimatter is one of the most exciting 
developments of the recent years. 



NEUTRINO OSCILLATIONS 

A second trace of ground unification at low energy is ex- 
pected -as discussed by Maiani - to be given by neutrino os- 
cillations. The masses of neutrinos , and their di fferences which 
determine oscillation frequency are expected to be of the order 

'm(v) X * 2 (q»«rk)/E mnif . eation S (lO'^l) eV 

a range which . could be explored through the study of cosmic ray 
neutrinos, in MUD's.as discussed by Rubbia.or through improved 
reactor experiments, as discussed by Fiorini. 

Neutrino oscillations have long be suspected to be at the 



- 3 06 



base of the solar neutrino puzzle,which was reviewed by Bahcall. 
A different opportunity to explore neutrino oscillations 
could be given by supernova explosions .These explosions should 
give rise to an intense burst of electron neutrinos, with en- 
ergies ranging up to 100 MeV, which can be detected in massi ve 
underground detectors (MUD). Under the neutrino oscillation 
hypothesis electron neutrinos are a superposition of different 
components, v., with different masses, m.^ . The different com- 
ponents would proceed at different velocity: 



V . = 



-('-*) 



For a very distant event the components would arrive at 
different times, so that the event would appear as a series of 
distinct sub-bursts. The record of such an event would yield 
precious information on the masses m- (from timing data), while 
a comparison of the intensity of the sub-bursts would allow a 
measurement of the relative weight (mixing angles) of the dif- 
ferent components in electron neutrinos. 



NUMBER OF NEUTRINO SPECIES 

Another argument which attracted a lot of attention is the 
possibility of obtaining - from Big Bang dynamics -information 
on the number of neutrino species. The basis of this is that 
the number of neutrino species determines the time it takes the 
universe to cool from 100 MeV, the temperature at which elec- 
tron neutrinos decouples from baryons, and lose the ability to 
keep equilibrium between protons and neutrons, to a temperature 
(~ lMeV) where free neutrons are captured by protons to form 
helium. 

The time lapse between these two temperatures (~3 minutes) 
determines how many neutrons survive beta decay and therefore 



- 307 



the abundance of "primordial" helium. 

Details of the argument where presented by Q. Steigman who, 
on some other occasion, has stated provocatively that the cos- 
mos is the ultimate accelerator. What clearly emerged from the 
different talks which were presented here is that the cosmos 
is a great store of unique information on particle interactions 
under extreme conditions, either of energy, as in the early 
universe, or of time of flight, as in the case of cosmic neu- 
trinos, or still in other ways yet to be conceived. It is clear 
that information is flowing both ways: advances in particles 
physics are laying the basis for the understanding of funda- 
mental astrophysi cal problems such as that of the predominance 
of matter over antimatter. 

In the specific case of the number of neutrino species, it 
is expected that this number can be di rect ly determined by meas - 
urements of Z production at large e e~ machines: when this is 
done we will have a new check on Big Bang dynamics. Could we 
turn the argument around, and say that accelerators can be the 
ultimate telescopes? Perhaps not, but. . . . 



- 309 



CONTRIBUTORS 



BAHCALL JOHN N. - School of Natural Sciences -The Institute for 
Advanced Study - PRINCETON, N.J. 08540 (U.S.A.) 

BALDO-CEOLIN MILLA - Universita degli Studi di Padova - Istituto 
di Fisica"Galileo Galilei"- Via F.Marzolo, 8- 35100 PADOVA 

CABIBBO NICOLA - Istituto di Fisica Teorica -Universita - Piaz- 
zale delle Scienze, 5 - 00185 ROMA 

CARAVEO PATRIZIA A. - L.F.C.T.R. - Via Bassini 15-20133 MILANO 

CARR BERNARD J. - Institute of Astronomy - The Observatories - 
Madingley Road - CAMBRIDGE CB3 OHA (Gran Bretagna) 

CAVALIERE ALFONSO - Istituto di Astrofisica Spaziale - C.N.R. - 
00044 FRASCATI (Roma) 

COCCONI GIUSEPPE - CERN - 1211 GENEVE 23 (Svizzera) 

ELLIS JOHN - CERN - 1211 GENEVE 23 (Svizzera) 

FIORINI ETTORE - Istituto di Fisica - Universita - Via Celo- 
ria, 16 - 20133 MILANO 

GIACCONI RICCARDO - Center for Astrophysics - Harvard College 
Observatory - Smithsonian Astrophy si cal Observatory 
60 Garden Street - CAMBRIDGE, Mass. 02138 (U.S.A.) 

GLASHOW SHELDON L. - Department of Physi cs - Harvard Uni versi ty - 
Lyman Laboratory of Physics - CAMBRIDGE, Mass. 021 38 (U.S.A.) 

MAIANI LUCIANO - Istituto di Fisi ca - Uni versi ta - Piazzale delle 
Scienze, 5 "- 00185 ROMA 

PACINI "FRANCO -Direttore Osservatorio Astrofisico di Arcetri - 
Largo Enrico Fermi, 5 - 50125 FIRENZE 



- 310 



RUBBIA CARLO - CERN - 1211 GENEVE 23 (Svizzera) 

RUDERMAN MALVIN - Institute of Astronomy - The Observatories - 
Madingley Road - CAMBRIDGE - CB3 OHA (Gran Bretagna) 

RUFFINI REMO - Istituto di Fisica -Universita* - Piazzale delle 
Scienze, 5 - 00185 ROMA 

SALVINI GIORGIO -Presidente del Centro Linceo Interdisciplina- 
re di Scienze Matematiche e loro Applicazioni - Via della 
Lungara, 10 - 00165 ROMA 

SCIAMA DENNIS W. - Department of Astrophysics - University Ob- 
servatory - South Parks Road - OXFORD 0X1 3RQ (Gran Bre- 
tagna) 

STEIGMAN GARY - Bartol Research Foundation of the Franklin Ins- 
titute - University of Delaware - NEWARK, Delaware 19711 
(U.S.A.). 



- 311 



CONTENTS 



PROGRAM Page 5 

G. SALVINI - Why this Meeting " 7 

S.L. GLASHOW - Astrophysics and Elementary Particles. Intro- 
ductory Talk " 11 

J.N. BAHCALL - Solar Neutrinos " 25 

M. RUDERMAN - Superdense Matter and Elementary Particle Phys- 
ics ' " 43 

G. STEIGMAN - As trophysical Constraints on Neutrino Physics " 67 

E. FIORINI - Neutrino Experiments in the Laboratory .Open Prob- 

lems "91 

L. MAIANI - Neutrino Oscillations " 121 

D.W.SCIAMA - The Anisotropy of the Cosmic Black Body Radia- 
tion and its Meaning 141 

J. ELLIS - Grand Unified Theories and the Very Early Universe " 153 

G. COCCONI - Big and Smaller Bangs Suggesting New Physics " 165 

B.J. CARR - TTie Origin of Entropy and Galaxy Formation " 177 

C. RUBBIA - Experiments with Elementary Particles Related to 
Cosmology: Neutrino Oscillations and Proton Life- 
time "205 

R. GIACCONI - X-ray Astronomy - Recent Results " 225 

M. BALDO-CEOLIN - Search for Neutron-Antineutron Oscillations " 251 

R. RUFFINI - On the Magnetosphere of Collapsed Stars " 259 

P. A. CARAVEO - Remark on the Speech of Prof. R.Ruffini " 263 

F. PACINI - The Activity of Galactic Nuclei " 265 

A. CAVALIERE - Physics of the Compact Sources in Active Galac- 
tic Nuclei and Quasars 275 

N. CABIBBO - Concluding Remarks " 2 99 

CONTRIBUTORS " 309 



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